### MA5890 Numerical Linear Algebra

#### Course Details

**Description:**

The course will focus on designing algorithms for matrix computations, analysing these algorithms (in terms of complexity, communication costs, stability, performance in finite precision and exact arithmetic), implementation on different computer architectures.

**CourseContent:**

Floating point arithmetic (1 lecture)

Stability of algorithms (2 lectures)

conditioning of a problem (2 lectures)

perturbation analysis (2 lectures)

algorithmic complexity (1 lecture)

Matrix decomposition including LU, Cholesky, QR, SVD, etc. (12 lectures)

Iterative techniques mainly focussing on Krylov subspace methods including Lanczos, Arnoldi, Conjugate Gradient, GMRES, etc. (12 lectures)

Preconditioning (2 lectures)

structured matrix computations (4 lectures)

designing matrix algorithms on modern computer architectures (3 lectures)

#### Course References:

TextBooks:

1. James W. Demmel, Applied Numerical Linear Algebra, Publisher : Society for Industrial and Applied Mathematics, Year : 1997

2. N. Trefethen & David Bau III, Numerical Linear Algebra, Publisher : Society for Industrial and Applied Mathematics, Year : 1997

ReferenceBooks:

1. Biswa Nath Datta, Numerical Linear Algebra and applications, 2nd Edition, Publisher : Society for Industrial and Applied Mathematics, Year : 2010

Prerequisite:

Linear Algebra at undergraduate level