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VITA
WALTER GAUTSCHI

April 17, 2012

EDUCATION


Ph.D. University of Basel, Switzerland 1953
  (Thesis advisor: A. M. Ostrowski)  


PROFESSIONAL EXPERIENCE


Research Fellow Istituto Nazionale per le  
  Applicazioni del Calcolo, Rome 1954-55
Research Fellow Harvard Computation Lab. 1955-56
Research Mathematician Natl. Bureau of Standards 1956-59
Professor. Lecturer American U., Washington, D.C.  
Mathematician Oak Ridge National Lab. 1959-63
Professor of Math.    
& Computer Science Purdue University 1963-2000
Professor Emeritus Purdue University 2000-
Visiting Professor Technical Univ. of Munich, Germany 1970-71
Visiting Professor Mathematics Res. Center, Univ. of WI 1976-77
Visiting Professor ETH Zurich 1996-2001
Visiting Professor University of Padova 1997
Visiting Professor University of Basel 2000

PROFESSIONAL SOCIETIES AND HONORS


Schweizerische Mathematische Gesellschaft
American Mathematical Society
Mathematical Association of America
Society for Industrial and Applied Mathematics
Corresponding Member, Bavarian Academy of Sciences, Munich, 2001-
Foreign Member, Academy of Sciences, Turin, 2001-
SIAM Fellow, Class 2012
Member, Council of the American Mathematical Society, 1975-80, 1984-95
Fulbright Research Scholar, Munich, 1970-71
Listed in Who is Who in the World
Listed in the International Biographical Centre's Top 100 Educators 2009 and in
    2000 Outstanding Intellectuals of the $21^{\rm st}$ Century
Listed in S. Gottwald, H.-J. Ilgauds, and K.-H. Schlote, Lexikon bedeutender
    Mathematiker, 2d ed., Verlag Programm Mathematik, Leipzig, in preparation.


RESEARCH INTERESTS


Numerical Analysis
Constructive Approximation Theory
Special Functions


GENERAL INFORMATION


Birthdate: December 11, 1927
Birthplace: Basel, Switzerland
Marital Status: Married - Erika
Children: 4
Citizenship: USA


PUBLICATIONS

Books

B1. (with H. Bavinck and G. M. Willems) Colloquium approximatietheorie, MC Syllabus 14, Mathematisch Centrum Amsterdam, 1971.
B2. Numerical analysis: an introduction, Birkhäuser, Boston, 1997. [2d edition, in preparation.]
B3. Orthogonal polynomials: computation and approximation, Oxford University Press, Oxford, 2004.

Proceedings Edited

P1. (with G. Allasia, L. Gatteschi, and G. Monegato) International conference on special functions: theory and computation, Rend. Sem. Mat. Univ. Politec. Torino, Special Issue, Università e Politecnico di Torino, Turin, 1985.
P2. Mathematics of Computation 1943-1993: a half-century of computational mathematics, Proc. Sympos. Appl. Math., v. 48, American Mathematical Society, Providence, RI, 1994 (xx + 643 pages).
P3. (with G. H. Golub and G. Opfer) Applications and computation of orthogonal polynomials, Internat. Ser. Numer. Math., v. 131, Birkhäuser, Basel, 1999 (xiv + 268 pages).
P4. (with F. Marcellán and L. Reichel) Numerical analysis 2000, Vol. 5: Quadrature and orthogonal polynomials, J. Comput. Appl. Math. 127, nos. 1-2 (2001).
P5. (with G. Mastroianni and Th. M. Rassias) Approximation and computation: in honor of Gradimir V. Milovanovic, Springer Optim. Appl., v. 42, Springer, Dordrecht, 2011.

Translations

T1. (with R. Bartels and C. Witzgall) Introduction to numerical analysis by J. Stoer and R. Bulirsch, translated from German, Springer, New York, 1980. [2d ed., Texts in Appl. Math., v. 12, Springer, New York, 1993.]
T2. Lectures on numerical mathematics by H. Rutishauser, annotated translation from German, Birkhäuser, Boston, 1990.
T3. (with Martin Mattmüller) Consideration of some series which are distinguished by special properties, Memoir E190 by Leonhard Euler, translated from Latin, http://math.
dartmouth.edu/~euler
T4. (with Erika Gautschi) Leonhard Euler by E .A. Fellmann, translated from German, Birkhäuser, Basel, 2007.

Refereed Papers

1951

  1. Ein Analogon zu Grammels Methode der graphischen Integration gewöhnlicher Differentialgleichungen, Z. Angew. Math. Mech. 31, 242-243.
1953
  1. Fehlerabschätzungen für die graphischen Integrationsverfahren von Grammel und
    Meissner-Ludwig    , Verh. Naturforsch. Ges. Basel 64, 401-435.
1954
  1. Über die zeichnerischen Ungenauigkeiten und die zweckmässige Bemessung der Schritt-
    länge beim graphischen Integrationsverfahren von Meissner-Ludwig    , Verh. Naturforsch.
    Ges. Basel 65, 49-66.
  2. Über eine Klasse von linearen Systemen mit konstanten Koeffizienten, Comment. Math.
    Helv. 28, 186-196.
1955
  1. Über den Fehler des Runge-Kutta-Verfahrens für die numerische Integration gewöhn-
    licher Differentialgleichungen n-ter Ordnung    , Z. Angew. Math. Phys. 6, 456-461.
1956
  1. Una estensione agli integrali doppi di una condizione di Picone necessaria per un estremo, Atti Accad. Naz. Lincei. Rend. Cl. Sci. Fis. Mat. Nat. (8) 20, 283-289.
  2. Bemerkung zu einer notwendigen Bedingung von Picone in der Variationsrechnung, Comment. Math. Helv. 31, 1-4.
  3. (with F. Malmborg) Calculations related to the improved free-volume-theory of liquids (AF Problem 116), Harvard Computation Laboratory, Problem Report 100, VI-1-VI-41.
1959
  1. Some elementary inequalities relating to the gamma and incomplete gamma function, J. Math. and Phys. 38, 77-81.
  2. Exponential integral $\int_1^\infty e^{-xt} t^{-n} dt$ for large values of n, J. Res. Nat. Bur. Standards 62, 123-125.
  3. Note on bivariate linear interpolation for analytic functions, Math. Tables Aids Comput. 13, 91-96.
1961
  1. Recursive computation of certain integrals, J. Assoc. Comput. Mach. 8, 21-40.
  2. Recursive computation of the repeated integrals of the error function, Math. Comp. 15, 227-232.
  3. Numerical integration of ordinary differential equations based on trigonometric polynomials, Numer. Math. 3, 381-397.
1962
  1. (with H. A. Antosiewicz) Numerical methods in ordinary differential equations, Ch. 9 in Survey of numerical analysis (J. Todd, ed.), 314-346, McGraw-Hill, New York.
  2. On inverses of Vandermonde and confluent Vandermonde matrices, Numer. Math. 4, 117-123.
  3. Diffusion functions for small argument, SIAM Rev. 4, 227-229.
1963
  1. Instability of linear second-order difference equations, in Proc. IFIP Congress 62 (C. M.
    Popplewell, ed.), 207, North-Holland, Amsterdam.
  2. On inverses of Vandermonde and confluent Vandermonde matrices II, Numer. Math. 5, 425-430.
1964
  1. (with W. F. Cahill) Exponential integral and related functions, Ch. 5 in Handbook of mathematical functions (M. Abramowitz and I. A. Stegun, eds.), 227-251, Nat. Bur.
    Standards Appl. Math. Ser. 55. [Russian translation by V. A. Ditkin and L. N. Karmazina, in Spravocnik po special'nym funkciyam, 55-79, Nauka, Moscow, 1979.]
  2. Error function and Fresnel integrals, Ch. 7 in Handbook of mathematical functions (M. Abramowitz and I. A. Stegun, eds.), 295-329, Nat. Bur. Standards Appl. Math. Ser.
    55.[Russian translation by V. A. Ditkin and L. N. Karmazina, in Spravocnik po special'nym funkciyam, 119-152, Nauka, Moscow, 1979.]
  3. Algorithm 221 -- Gamma function, and Algorithm 222 -- Incomplete beta function ratios, Comm. ACM 7, 143-144; Certification of Algorithm 222, ibid., 244.
1965
  1. Algorithm 236 -- Bessel functions of the first kind, Comm. ACM 7, 479-480; Certification of Algorithm 236, ibid. 8, 105-106.
  2. Algorithm 259 -- Legendre functions for arguments larger than one, Comm. ACM 8, 488-492.
1966
  1. Computation of transcendental functions by recurrence relations, in Proc. IFIP Congress 65, v. 2 (W. A. Kalenich, ed.), 485-486, Spartan Books, Washington, D. C.
  2. Computation of successive derivatives of $f(z)/z$, Math. Comp. 20, 209-214.
  3. Algorithm 282 -- Derivatives of $e^x /x$, $\cos (x)/x$, and $\sin (x)/x$, Comm. ACM 9, 272.
  4. Algorithm 292 -- Regular Coulomb wave functions, Comm. ACM 9, 793-795.
1967
  1. Computational aspects of three-term recurrence relations, SIAM Rev. 9, 24-82.
  2. Numerical quadrature in the presence of a singularity, SIAM J. Numer. Anal. 4, 357-362.
1968
  1. Construction of Gauss-Christoffel quadrature formulas, Math. Comp. 22, 251-270.
  2. Algorithm 331 -- Gaussian quadrature formulas, Comm. ACM 11, 432-436.
1969
  1. Remark on Algorithm 292, Comm. ACM 12, 280.
  2. On the condition of a matrix arising in the numerical inversion of the Laplace transform, Math. Comp. 23, 109-118.
  3. An application of minimal solutions of three-term recurrences to Coulomb wave functions, Aequationes Math. 2, 171-176; abstract, ibid. 1 (1968), 208.
  4. Algorithm 363 -- Complex error function, Comm. ACM 12, 635.
1970
  1. (with B. J. Klein) Recursive computation of certain derivatives -- a study of error propagation, Comm. ACM 13, 7-9.
  2. (with B. J. Klein) Remark on Algorithm 282, Comm. ACM 13, 53-54.
  3. Efficient computation of the complex error function, SIAM J. Numer. Anal. 7, 187-198.
  4. On the construction of Gaussian quadrature rules from modified moments, Math. Comp.
    24, 245-260.
1971
  1. Attenuation factors in practical Fourier analysis, Numer. Math. 18, 373-400.
1972
  1. Zur Numerik rekurrenter Relationen, Computing 9, 107-126. [English translation in: Aerospace Research Laboratories, Report ARL 73-0005, February 1973.]
  2. The condition of orthogonal polynomials, Math. Comp. 26, 923-924.
1973
  1. Algorithm 471 -- Exponential integrals, Comm. ACM 16, 761-763.
  2. On the condition of algebraic equations, Numer. Math. 21, 405-424.
1974
  1. (with H. Yanagiwara) On Chebyshev-type quadratures, Math. Comp. 28, 125-134.
  2. A harmonic mean inequality for the gamma function, SIAM J. Math. Anal. 5, 278-281.
  3. Some mean value inequalities for the gamma function, SIAM J. Math. Anal. 5, 282-292.
1975
  1. Computational methods in special functions -- a survey, in Theory and applications of special functions (R. A. Askey, ed.), 1-98, Math. Res. Center, Univ. Wisconsin Publ., no. 35, Academic Press, New York.
  2. Nonexistence of Chebyshev-type quadratures on infinite intervals, Math. Comp. 29, 93-99.
  3. Norm estimates for inverses of Vandermonde matrices, Numer. Math. 23, 337-347.
  4. Optimally conditioned Vandermonde matrices, Numer. Math. 24, 1-12.
  5. (with L. A. Anderson) Optimal weighted Chebyshev-type quadrature formulas, Calcolo 12, 211-248.
  6. Stime dell'errore globale nei metodi ``one-step'' per equazioni differenziali ordinarie, Rend. Mat. (2) 8, 601-617.
1976
  1. Advances in Chebyshev quadrature, in Numerical analysis (G. A. Watson, ed.), 100-121, Lecture Notes Math., v. 506, Springer, Berlin.
  2. Comportement asymptotique des coefficients dans les formules d'intégration d'Adams, de Störmer et de Cowell, C. R. Acad. Sci. Paris Ser. A-B 283, A787-A788.
  3. Qualche contributo recente sul problema di Chebyshev nella teoria dell'integrazione numerica, Rend. Sem. Mat. Univ. e Politec. Torino 35, 39-44.
1977
  1. (with G. Monegato) On optimal Chebyshev-type quadratures, Numer. Math. 28, 59-67.
  2. Evaluation of the repeated integrals of the coerror function, ACM Trans. Math. Software 3, 240-252.
  3. Algorithm 521 -- Repeated integrals of the coerror function, ACM Trans. Math. Software 3, 301-302.
  4. Anomalous convergence of a continued fraction for ratios of Kummer functions, Math.
    Comp. 31, 994-999.
1978
  1. On inverses of Vandermonde and confluent Vandermonde matrices III, Numer. Math. 29, 445-450.
  2. (with J. Slavik) On the computation of modified Bessel function ratios, Math. Comp. 32, 865-875.
  3. Questions of numerical condition related to polynomials, in Symposium on recent advances in numerical analysis (C. de Boor and G. H. Golub, eds.), 45-72, Academic Press, New York. [Revised and reprinted in MAA Studies in Mathematics, v. 24: Studies in numerical analysis (G. H. Golub, ed.), 140-177, Math. Assoc. America, Washington, DC, 1984.]
1979
  1. On generating Gaussian quadrature rules, in Numerische Integration (G. Hämmerlin, ed.), 147-154, Internat. Ser. Numer. Math., v. 45, Birkhäuser, Basel.
  2. The condition of polynomials in power form, Math. Comp. 33, 343-352.
  3. On the preceding paper ``A Legendre polynomial integral'' by James L. Blue, Math.
    Comp. 33, 742-743.
  4. A computational procedure for incomplete gamma functions, ACM Trans. Math. Software 5, 466-481.
  5. Algorithm 542 -- Incomplete gamma functions, ACM Trans. Math. Software 5, 482-489.
  6. Un procedimento di calcolo per le funzioni gamma incomplete, Rend. Sem. Mat. Univ. e Politec. Torino 37, 1-9.
  7. Families of algebraic test equations, Calcolo 16, 383-398.
1980
  1. (with F. Costabile) Stime per difetto per gli zeri più grandi dei polinomi ortogonali, Boll. Un. Mat. Ital. (5) 17A, 516-522.
  2. (with M. Montrone) Metodi multistep con minimo coefficiente dell'errore globale, Calcolo 17, 67-75.
1981
  1. A survey of Gauss-Christoffel quadrature formulae, in E. B. Christoffel -- the influence of his work in mathematics and the physical sciences (P. L. Butzer and F. Fehér, eds.), 72-147, Birkhäuser, Basel.
  2. Minimal solutions of three-term recurrence relations and orthogonal polynomials, Math.
    Comp. 36, 547-554.
  3. Recognition of Christoffel's work on quadrature during and after his lifetime, in E. B.
    Christoffel -- the influence of his work in mathematics and the physical sciences     (P. L. Butzer and F. Fehér, eds.), 724-727, Birkhäuser, Basel.
1982
  1. An algorithmic implementation of the generalized Christoffel theorem, in Numerical integration (G. Hämmerlin, ed.), 89-106, Internat. Ser. Numer. Math., v. 57, Birkhäuser, Basel.
  2. (with R. E. Lynch) Error behavior in optimal relaxation methods, Z. Angew. Math. Phys.
    33, 24-35.
  3. A note on the successive remainders of the exponential series, Elem. Math. 37, 46-49.
  4. Polynomials orthogonal with respect to the reciprocal gamma function, BIT 22, 387-389.
  5. On generating orthogonal polynomials, SIAM J. Sci. Statist. Comput. 3, 289-317.
1983
  1. To Alexander M. Ostrowski on his ninetieth birthday, Linear Algebra Appl. 52/53, xi-xiv.
  2. The condition of Vandermonde-like matrices involving orthogonal polynomials, Linear Algebra Appl. 52/53, 293-300.
  3. How and how not to check Gaussian quadrature formulae, BIT 23, 209-216.
  4. (with R. S. Varga) Error bounds for Gaussian quadrature of analytic functions, SIAM J. Numer. Anal. 20, 1170-1186.
  5. On Padé approximants associated with Hamburger series, Calcolo 20, 111-127.
  6. On the convergence behavior of continued fractions with real elements, Math. Comp. 40, 337-342.
1984
  1. (with G. V. Milovanovic) On a class of complex polynomials having all zeros in a half circle, in Numerical methods and approximation theory (G. V. Milovanovic, ed.), 49-53, Faculty of Electronic Engineering, Univ. Niš, Niš.
  2. Discrete approximations to spherically symmetric distributions, Numer. Math. 44, 53-60.
  3. On some orthogonal polynomials of interest in theoretical chemistry, BIT 24, 473-483.
  4. (with Jet Wimp) In memoriam YUDELL L. LUKE June 26, 1918 - May 6, 1983, Math. Comp. 43, 349-352.
1985
  1. Some new applications of orthogonal polynomials, in Polynômes orthogonaux et applications (C. Brezinski, A. Draux, A. P. Magnus, P. Maroni and A. Ronveaux, eds.), 63-73, Lecture Notes Math., v. 1171, Springer, Berlin.
  2. (with G. V. Milovanovic) Gaussian quadrature involving Einstein and Fermi functions with an application to summation of series, Math. Comp. 44, 177-190. Supplement, ibid., S1-S11.
  3. Orthogonal polynomials -- constructive theory and applications, J. Comput. Appl. Math.
    12/13, 61-76.
  4. (with G. V. Milovanovic) Polynomials orthogonal on the semicircle, Rend. Sem. Mat.
    Univ. e Politec. Torino, Special Issue, 179-185.
1986
  1. (with B. Flury) An algorithm for simultaneous orthogonal transformation of several positive definite matrices to nearly diagonal form, SIAM J. Sci. Statist. Comput. 7, 169-184.
  2. (with G. V. Milovanovic) Polynomials orthogonal on the semicircle, J. Approx. Theory 46, 230-250.
  3. On the sensitivity of orthogonal polynomials to perturbations in the moments, Numer. Math. 48, 369-382.
  4. (with F. Caliò and E. Marchetti) On computing Gauss-Kronrod quadrature formulae, Math. Comp. 47, 639-650.
  5. (with G. V. Milovanovic) Spline approximations to spherically symmetric distributions, Numer. Math. 49, 111-121.
  6. Reminiscences of my involvement in de Branges's proof of the Bieberbach conjecture, in The Bieberbach conjecture (Albert Baernstein II, David Drasin, Peter Duren, and Albert Marden, eds.), 205-211, Proc. Symp. on the Occasion of the Proof, Math. Surveys Monographs, no. 21, American Mathematical Society, Providence, RI.
1987
  1. (with M. Frontini and G. V. Milovanovic) Moment-preserving spline approximation on finite intervals, Numer. Math. 50, 503-518.
  2. (with J. Wimp) Computing the Hilbert transform of a Jacobi weight function, BIT 27, 203-215.
  3. (with H. J. Landau and G. V. Milovanovic) Polynomials orthogonal on the semicircle II, Constructive Approx. 3, 389-404.
  4. (with M. A. Kovacevic and G. V. Milovanovic) The numerical evaluation of singular integrals with coth-kernel, BIT 27, 389-402.
  5. A conjectured inequality for Hermite interpolation at the zeros of Jacobi polynomials, Problem 87-7, SIAM Rev. 29, 297-298.
1988
  1. Gauss-Kronrod quadrature -- a survey, in Numerical methods and approximation theory III (G. V. Milovanovic, ed.), 39-66, Faculty of Electronic Engineering, Univ. Niš, Niš.
  2. (with S. E. Notaris) Newton's method and Gauss-Kronrod quadrature, in Numerical integration III (H. Brass and G. Hämmerlin, eds.), 60-71, Internat. Ser. Numer. Math., v. 85, Birkhäuser, Basel.
  3. (with S. E. Notaris) An algebraic study of Gauss-Kronrod quadrature formulae for Jacobi weight functions, Math. Comp. 51, 231-248.
  4. (with G. Inglese) Lower bounds for the condition number of Vandermonde matrices, Numer. Math. 52, 241-250.
  5. (with T. J. Rivlin) A family of Gauss-Kronrod quadrature formulae, Math. Comp. 51, 749-754.
1989
  1. Orthogonality -- conventional and unconventional -- in numerical analysis, in Computation and control (K. Bowers and J. Lund, eds.), 63-95, Progress in Systems and Control Theory, v. 1, Birkhäuser, Boston.
  2. On the zeros of polynomials orthogonal on the semicircle, SIAM J. Math. Anal. 20, 738-743.
  3. (with S. E. Notaris) Gauss-Kronrod quadrature formulae for weight functions of Bernstein-Szegö type, J. Comput. Appl. Math. 25, 199-224. [Erratum, ibid. 27 (1989), 429.]
1990
  1. Some applications and numerical methods for orthogonal polynomials, in Numerical analysis and mathematical modelling (A. Wakulicz, ed.), 7-19, Banach Center Publications, v. 24, PWN Polish Scientific Publishers, Warsaw.
  2. Orthogonal polynomials on the semicircle, in Numerical analysis and mathematical modelling (A. Wakulicz, ed.), 21-27, Banach Center Publications, v 24, PWN Polish Scientific Publishers, Warsaw.
  3. Computational aspects of orthogonal polynomials, in Orthogonal polynomials (Paul Nevai, ed.), 181-216, NATO ASI Series, Series C: Mathematical and Physical Sciences, v. 294, Kluwer, Dordrecht.
  4. How (un)stable are Vandermonde systems?, in Asymptotic and computational analysis (R. Wong, ed.), 193-210, Lecture Notes Pure Appl. Math., v. 124, Dekker, New York.
  5. (with E. Tychopoulos and R.S. Varga) A note on the contour integral representation of the remainder term for a Gauss-Chebyshev quadrature rule, SIAM J. Numer. Anal. 27, 219-224.
  6. (with A. Córdova and S. Ruscheweyh) Vandermonde matrices on the circle: spectral properties and conditioning, Numer. Math. 57, 577-591.
  7. (with Shikang Li) The remainder term for analytic functions of Gauss-Radau and Gauss-Lobatto quadrature rules with multiple end points, J. Comput. Appl. Math. 33, 315-329.
1991
  1. Computational problems and applications of orthogonal polynomials, in Orthogonal polynomials and their applications (C. Brezinski, L. Gori and A. Ronveaux, eds.), 61-71, IMACS Annals Comput. Appl. Math., v. 9, Baltzer, Basel.
  2. On the remainder term for analytic functions of Gauss-Lobatto and Gauss-Radau quadratures, Rocky Mountain J. Math. 21, 209-226.
  3. A class of slowly convergent series and their summation by Gaussian quadrature, Math. Comp. 57, 309-324.
  4. On certain slowly convergent series occurring in plate contact problems, Math. Comp. 57, 325-338.
  5. (with Shikang Li) Gauss-Radau and Gauss-Lobatto quadratures with double end points, J. Comput. Appl. Math. 34, 343-360.
  6. On the paper ``A continued fraction approximation of the modified Bessel function
    $I_1 (t)$'' by P .R. Parthasarathy and N. Balakrishnan, Appl. Math. Letters 4, 47-51.
  7. Quadrature formulae on half-infinite intervals, BIT 31, 438-446.
1992
  1. Remainder estimates for analytic functions, in Numerical integration (T. O. Espelid and A. Ganz, eds.), 133-145, NATO ASI Series, Series C: Mathematical and Physical Sciences, v. 357, Kluwer, Dordrecht.
  2. Applications and computation of orthogonal polynomials, Proc. Eighteenth South African Sympos. Numer. Math. (S. Abelman, ed.), 47-71, Department of Computer Science, University of Natal, Durban.
  3. Spline approximation and quadrature formulae, Atti Sem. Mat. Fis. Univ. Modena 40, 169-182.
  4. On mean convergence of extended Lagrange interpolation, J. Comput. Appl. Math. 43, 19-35.
1993
  1. The spiral of Theodorus, special functions, and numerical analysis, Supplement A in Spirals: from Theodorus to chaos by P. J. Davis, 67-87, A K Peters, Boston.
  2. (with Shikang Li) A set of orthogonal polynomials induced by a given orthogonal polynomial, Aequationes Math. 46, 174-198.
  3. Is the recurrence relation for orthogonal polynomials always stable?, BIT 33, 277-284.
  4. On the computation of generalized Fermi-Dirac and Bose-Einstein integrals, Comput. Phys. Comm. 74, 233-238.
  5. Gauss-type quadrature rules for rational functions, in Numerical integration IV (H. Brass and G. Hämmerlin, eds.), 111-130, Internat. Ser. Numer. Math., v.112, Birkhäuser, Basel.
  6. (with S. E. Notaris) Problem 6, in Numerical integration IV (H. Brass and G. Hämmerlin, eds.), 379-380, Internat. Ser. Numer. Math., v. 112, Birkhäuser, Basel.
1994
  1. Summation of slowly convergent series, in Numerical analysis and mathematical modelling (A. Wakulicz, ed.), 7-18, Banach Center Publications, v. 29, PWN Polish Scientific Publishers, Warsaw.
  2. Applications and computation of orthogonal polynomials, in Advances in computational mathematics: New Delhi, India (H. P. Dikshit and C. A. Micchelli, eds.), Series in Approximations and Decompositions, v. 4, World Scientific, Singapore.
  3. Algorithm 726: ORTHPOL -- a package of routines for generating orthogonal polynomials and Gauss-type quadrature rules, ACM Trans. Math. Software 20, 21-62; Remark on Algorithm 726, ibid. 24 (1998), 355.
  4. Reflections and recollections, in Approximation and computation: a festschrift in honor of Walter Gautschi (R. V. M. Zahar, ed.), xvii-xxxv, Internat. Ser. Numer. Math., v. 119, Birkhäuser, Basel.
1995
  1. The work of Philip Rabinowitz on numerical integration, Numer. Algorithms 9, 199-222.
  2. Luigi Gatteschi's work on special functions and numerical analysis, Annals Numer.
    Math. 2, 3-19.
  3. (with M. Zhang) Computing orthogonal polynomials in Sobolev spaces, Numer. Math. 71, 159-183.
1996
  1. Orthogonal polynomials: applications and computation, Acta Numerica 1996 (A. Iserles, ed.), 45-119, Cambridge University Press, Cambridge.
  2. (with Shikang Li) On quadrature convergence of extended Lagrange interpolation, Math.
    Comp. 65, 1249-1256.
  3. (with S. E. Notaris) Stieltjes polynomials and related quadrature formulae for a class of weight functions, Math. Comp. 65, 1257-1268.
1997
  1. (with J. Waldvogel) Contour plots of analytic functions, Ch. 25 in Solving problems in scientific computing using Maple and Matlab (W. Gander and J. Hrebícek, eds.), 3d ed., 359-372, Springer, Berlin. [Chinese translation by China Higher Education Press and Springer, 1999; Portuguese translation of 3d ed. by Editora Edgard Blücher Ltda, Sao Paolo, 2001; Russian translation of 4th ed. by Vassamedia, Minsk, Bjelarus, 2005.]
  2. The computation of special functions by linear difference equations, in Advances in difference equations (S. Elaydi, I. Gyori, and G. Ladas, eds.), 213-243, Gordon and Breach, Amsterdam.
  3. On the computation of special Sobolev-type orthogonal polynomials, The heritage of P. L. Chebyshev: a festschrift in honor of the 70th birthday of T. J. Rivlin, Ann. Numer. Math. 4, 329-342.
  4. Moments in quadrature problems, Approximation theory and approximation, Comput. Math. Appl. 33, 105-118.
  5. (with A. B. J. Kuijlaars) Zeros and critical points of Sobolev orthogonal polynomials, J. Approx. Theory 91, 117-137.
  6. (with G. V. Milovanovic) s-orthogonality and construction of Gauss-Turán-type quadrature formulae, J. Comput. Appl. Math. 86, 205-218.
1998
  1. The incomplete gamma functions since Tricomi, in Tricomi's ideas and contemporary applied mathematics, 203-237, Atti dei Convegni Lincei, n. 147, Accademia Nazionale dei Lincei, Roma.
  2. Ostrowski and the Ostrowski prize, Math. Intelligencer 20, 32-34. [Revised and translated into German, Uni Nova 87 (2000), 60-62, Universität Basel.]
1999
  1. Orthogonal polynomials and quadrature, Electron. Trans. Numer. Anal. 9, 65-76.
  2. A note on the recursive calculation of incomplete gamma functions, ACM Trans. Math.
    Software 25, 101-107.
  3. Algorithm 793: GQRAT -- Gauss quadrature for rational functions, ACM Trans. Math.
    Software 25, 213-239.
2000
  1. (with W. Gander) Adaptive quadrature -- revisited, BIT 40, 84-101.
  2. (with L. Gori and F. Pitolli) Gauss quadrature for refinable weight functions, Appl. Comput. Harmon. Anal. 8, 249-257.
  3. (with L. Gori and M. L. Lo Cascio) Quadrature rules for rational functions, Numer. Math. 86, 617-633.
  4. High-order Gauss-Lobatto formulae, Numer. Algorithms 25, 213-222.
  5. Gauss-Radau formulae for Jacobi and Laguerre weight functions, Math. Comput. Simulation 54, 403-412. [Reprinted in Computational Science, Mathematics and Software (Ronald F. Boisvert and Elias Houstis, eds.), 237-248, Purdue University Press, West Lafayette, IN.]
2001
  1. Remark on the paper ``Barycentric formulae for cardinal (SINC-) interpolants'' by Jean-Paul Berrut, Numer. Math. 87, 791-792.
  2. (with J. Waldvogel) Computing the Hilbert transform of the generalized Laguerre and Hermite weight functions, BIT 41, 490-503.
  3. The use of rational functions in numerical quadrature, J. Comput. Appl. Math. 133, 111-126.
2002
  1. Gauss quadrature approximations to hypergeometric and confluent hypergeometric functions, J. Comput. Appl. Math. 139, 173-187.
  2. Computation of Bessel and Airy functions and of related Gaussian quadrature formulae, BIT 42, 110-118.
  3. The interplay between classical analysis and (numerical) linear algebra -- a tribute to Gene H. Golub, Electron. Trans. Numer. Anal. 13, 119-147.
  4. Alessandro M. Ostrowski (1893-1986). La sua vita e le opere, Boll. Docenti Matem. 45, 9-19.
2003
  1. (with F. E. Harris and N. M. Temme) Expansions of the exponential integral in incomplete gamma functions, Appl. Math. Lett. 16, 1095-1099.
2004
  1. Generalized Gauss-Radau and Gauss-Lobatto formulae, BIT 44, 711-720.
2005
  1. Orthogonal polynomials (in Matlab), J. Comput. Appl. Math. 178, 215-234.
  2. The Hardy-Littlewood function: an exercise in slowly convergent series, J. Comput.
    Appl. Math. 179, 249-254.
  3. Computing polynomials orthogonal with respect to densely oscillating and exponentially decaying weight functions and related integrals, J. Comput. Appl. Math. 184, 493-504.
  4. A historical note on Gauss-Kronrod quadrature, Numer. Math. 100, 483-484.
  5. Numerical quadrature computation of the Macdonald function for complex orders, BIT Numer. Math. 45, 593-603.
2006
  1. Orthogonal polynomials, quadrature, and approximation: computational methods and software (in Matlab), in Orthogonal polynomials and special functions -- computation and applications (Francisco Marcellán and Walter Van Assche, eds.), 1-77, Lecture Notes Math. 1883.
  2. The circle theorem and related theorems for Gauss-type quadrature rules, Electron. Trans.
    Numer. Anal. 25, 129-137.
  3. Computing the Kontorovich-Lebedev integral transforms and their inverses, BIT Numer. Math. 46, 21-40.
2007
  1. (with Paul Leopardi) Conjectured inequalities for Jacobi polynomials and their largest zeros, Numer. Algorithms 45, 217-230.
  2. Leonhard Eulers Umgang mit langsam konvergenten Reihen, Elem. Math. 62, 174-183.
  3. Commentary, in Milestones in matrix computation: selected works of Gene H. Golub, with commentaries (Raymond H. Chan, Chen Greif, and Dianne P. O'Leary, eds.), 345-358, Oxford University Press, New York.
  4. A guided tour through my bibliography, Numer. Algorithms 45, 11-35.
2008
  1. On Euler's attempt to compute logarithms by interpolation: a commentary to his letter of February 16, 1734 to Daniel Bernoulli, J. Comput. Appl. Math. 219, 408-415.
  2. Leonhard Euler: his life, the man, and his work, SIAM Rev. 50, 3-33. [Also published in ICIAM 07, $6^{\rm {th}}$ International Congress on Industrial and Applied Mathematics, Zürich, Switzerland, 16-20 July 2007 (Rolf Jeltsch and Gerhard Wanner, eds.), 447-483, European Mathematical Society, 2009. Chinese translation in Mathematical Advance in Translation (2008)(2-3).]
  3. The numerical evaluation of a ``challenging'' integral, Numer. Algorithms 49, 187-194.
  4. (with Carla Giordano) Luigi Gatteschi's work on asymptotics of special functions and their zeros, Numer. Algorithms 49, 11-31.
  5. On a conjectured inequality for the largest zero of Jacobi polynomials, Numer. Algorithms 49, 195-198.
2009
  1. On conjectured inequalities for zeros of Jacobi polynomials, Numer. Algorithms 50, 93-96.
  2. New conjectured inequalities for zeros of Jacobi polynomials, Numer. Algorithms 50, 293-296.
  3. How sharp is Bernstein's inequality for Jacobi polynomials?, Electr. Trans. Numer. Anal.
    36, 1-8.
  4. High-order generalized Gauss-Radau and Gauss-Lobatto formulae for Jacobi and Laguerre weight functions, Numer. Algorithms 51, 143-149.
  5. Variable-precision recurrence coefficients for nonstandard orthogonal polynomials, Numer. Algorithms 52, 409-418.
2010
  1. Alexander M. Ostrowski (1893-1986): his life, work, and students, in math.ch/100 Swiss Mathematical Society 1910-2010 (Bruno Colbois, Christine Riedtmann, and Viktor Schroeder, eds.), 257-278, European Mathematical Society.
  2. The spiral of Theodorus, numerical analysis, and special functions, J. Comput. Appl.
    Math. 235, 1042-1052.
  3. Gauss quadrature routines for two classes of logarithmic weight functions, Numer. Algorithms 55, 265-277.
2011
  1. The Lambert W-functions and some of their integrals: a case study of high-precision computation, Numer. Algorithms 57, 27-34.
  2. Optimally scaled and optimally conditioned Vandermonde and Vandermonde-like matrices, BIT Numer. Math. 51, 103-125.
  3. My collaboration with Gradimir V. Milovanovic, in Approximation and computation -- in honor of Gradimir V. Milovanovic (Walter Gautschi, Giuseppe Mastroianni, and Themistocles M. Rassias, eds.), 33-43, Springer Optim. Appl., v. 42, Springer, Dordrecht.
  4. Experimental mathematics involving orthogonal polynomials, in Approximation and computation -- in honor of Gradimir V. Milovanovic (Walter Gautschi, Giuseppe Mastroianni, and Themistocles M. Rassias, eds.), 115-131, Springer Optim. Appl., v. 42, Springer, Dordrecht.
  5. Remark on ``New conjectured inequalities for zeros of Jacobi polynomials'' by Walter Gautschi, Numer. Algorithms 50: 293-296 (2009), Numer. Algorithms 57, 511.
2012
  1. Sub-range Jacobi polynomials, Numer. Algorithms, to appear.
  2. Kommentar 7 zum Brief Nr. 9 von Leonhard Euler an Daniel Bernoulli, Briefwechsel Eulers mit Daniel Bernoulli, Opera Omnia, ser. IVA, v. 3, Birkhäuser, Basel. [In preparation.]
  3. Repeated modifications of orthogonal polynomials by linear divisors, submitted.
  4. Numerical integration over the square in the presence of algebraic/logarithmic singularities with an application to aerodynamics, submitted.


RESEARCH GRANTS

  1. National Science Foundation, Research in numerical analysis,

    6/1/76 - 5/31/78, $25,700.

  2. National Science Foundation, Gauss type quadrature rules,

    6/1/80 - 5/31/82, $39,171.

  3. National Science Foundation, Applied orthogonal polynomials,

    6/1/82 - 7/31/90, $303,607.

  4. National Science Foundation, Mathematical sciences: applied orthogonal polynomials,

    6/1/91 - 11/30/93, $107,500.

  5. National Science Foundation, Mathematical sciences: orthogonal polynomials - applications and computation,

    6/1/94 - 12/31/95, $90,000.


PROFESSIONAL ACTIVITIES


Reviewer for Mathematical Reviews 1956-
Consultant, Argonne National Laboratory 1967-77
C.I.M.E. Lecturer, Perugia, Italy 1965
ACM National Lecturer 1966-67
SIAM Visiting Lecturer 1971-72, 1975-76
Invited Lecturer, Summer Courses in Mathematics, Perugia 1972, 1973
and Cortona, Italy 1974, 1975
  1977, 1980
  1981, 1986
  1994
Member, Stiftungsrat of the A.M. Ostrowski Foundation  
for an International Prize in Higher Mathematics 1995 -
Member, 1999 Henrici Prize Committee 1999


EDITORSHIPS


Editorial Committee, Mathematics of Computation 1966-1999
Managing Editor 1984-1995
Editorial Board, SIAM Journal on Mathematical Analysis 1970-73
Editorial Board, Numerische Mathematik 1971-
Honorary Editor 1991-
Editorial Board, Calcolo 1975-1987
Special Editor, Linear Algebra and its Applications 1981-83


Ph.D. STUDENTS


Ramsey Vincent Michel Zahar (1968)
James Lincoln Phillips (1969)
Larry Arnold Anderson (1974)
Ja-Chen Lin (1988)
Sotirios E. Notaris (1988)
Shikang Li (1992)
Minda Zhang (1993)


POSTGRADUATE STUDENTS


Hiroki Yanagiwara, Japan (1971-72)

Giovanni Monegato, Italy (1974-76)

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VITA
WALTER GAUTSCHI

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