Topic: RandNLA: Randomization in Numerical Linear Algebra
Lecturer: Petros Drineas, Purdue University
TA: Peng Xu, Stanford University
The introduction of randomization in the design and analysis of
algorithms for matrix computations (such as matrix multiplication,
least-squares regression, the Singular Value Decomposition (SVD), etc.)
over the past 15 years provided a new paradigm and a complementary
perspective to traditional numerical linear algebra approaches. These
novel approaches were motivated by technological developments in many
areas of scientific research that permit the automatic generation of
large data sets, which are often modeled as matrices. We will outline
how such approaches can be used to approximately solve problems ranging
from matrix multiplication and the Singular Value Decomposition (SVD)
of matrices to the Column Subset Selection Problem and the CX
decomposition. Application of the proposed algorithms to data analysis
tasks (with a particular focus in population genetics) will also be
discussed.
Background material
Take a look at our recent article (joint with M. W. Mahoney) at the Communications of the ACM for an overview of RandNLA; take a look at the associated video synopsis as well.
Lecture slides (last updated Jul 5, 2016)
Introduction to Numerical Linear Algebra: Part I
Introduction to Numerical Linear Algebra: Part II
Randomization in Numerical Linear Algebra (four lectures)
TA Sessions (last updated Jun 24, 2016)
TA Session I
TA Session II
TA Session III
TA Session IV
TA Session V
Remark: The instructor and the TA may update the Lecture slides and the Homeworks to include additional material, fix typos, etc.