PCMI Graduate Summer School 2016: The Mathematics of Data

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.