Numerical Linear Algebra

Code: MA571 | L-T-P-C: 3-0-2-8

Prerequisites: MA522 Linear Algebra

Fundamentals - overview of matrix computations, norms of vectors and matrices, singular value decomposition (SVD), IEEE floating point arithmetic, analysis of roundoff errors, stability and ill-conditioning; Linear systems - LU factorization, Gaussian eliminations, Cholesky factorization, stability and sensitivity analysis; Jacobi, Gauss-Seidel and successive overrelaxation methods; Linear least-squares - Gram- Schmidt orthonormal process, rotators and reflectors, QR factorization, stability of QR factorization; QR method linear least-squares problems, normal equations, Moore- Penrose inverse, rank deficient least-squares problems, sensitivity analysis. Eigenvalues and singular values - Schur's decomposition, reduction of matrices to Hessenberg and tridiagonal forms; Power, inverse power and Rayleigh quotient iterations; QR algorithm, implementation of implicit QR algorithm; Sensitivity analysis of eiegnvalues; Reduction of matrices to bidiagonal forms, QR algorithm for SVD.

Software Support: MATLAB.

Texts:

1. L. N. Trefethen and David Bau, Numerical Linear Algebra, SIAM, 1997.
2. D. S. Watkins, Fundamentals of Matrix Computation, 2nd Edn., Wiley, 2002.

References:

1. J.W. Demmel, Applied Numerical Linear Algebra, SIAM, 1997.
2. B. N. Datta, Numerical Linear Algebra and Applications, 2nd Edn., SIAM, 2010.
3. G. H. Golub and C.F.Van Loan, Matrix Computation, 3rd Edn., Hindustan book agency, 2007.