Matrix Computation

Code: MA3121 | L-T-P-C: 3-0-2-8

Floating point computations, IEEE floating point arithmetic, analysis of round off errors; Sensitivity analysis and condition numbers; Linear systems, LU decompositions, Gaussian elimination with partial pivoting; Banded systems, positive definite systems, Cholesky decomposition - sensitivity analysis; Gram-Schmidt orthonormal process, Householder transformation, Givens rotations; QR factorization, stability of QR factorization. Solution of linear least squares problems, normal equations, singular value decomposition(SVD), polar decomposition, Moore-Penrose inverse; Rank deficient least-squares problems; Sensitivity analysis of least-squares problems; Review of canonical forms of matrices; Sensitivity of eigenvalues and eigenvectors. Reduction to Hessenberg and tridiagonal forms; Power, inverse power and Rayleigh quotient iterations; Explicit and implicit QR algorithms for symmetric and nonsymmetric matrices; Reduction to bidiagonal form; Golub-Kahan algorithm for computing SVD.

Texts:

• D. S. Watkins, Fundamentals of Matrix Computations, Second Edition, John Wiley, 2002.
• L. N. Trefethen and D. Bau, Numerical Linear Algebra, SIAM, 1997.

 

References:

• J. W. Demmel, Applied Numerical Linear Algebra, SIAM, 1997.
• M. L. Overton, Numerical Computing with IEEE Floating Point Arithmetic, SIAM, 2001.