Table of Contents

Introductory Material. Vector and matrices norms. Eigenvalues. Irreducibility and diagonal dominance. M--Matrices and generalizations. Splittings. Positive definite matrices. The graph of a matrix. Chebyshev polynomials Discretization methods for partial diffential equations. Eigenvalues and Fourier analysis. Floating point arithmetic. Vector and parallel computers. BLAS and LAPACK. Bibliographical comments. Gaussian elimination for general linear systems. Introduction to Gaussian elimination. Gaussian elimination without permutations. Gaussian elimination with permutations (partial piv- oting). Gaussian elimination with other pivoting strategies. Operation counts. Gaussian elimination for symmetric systems. The outer product algorithm. The bordering algorithm. The inner product algorithm. Coding the three factorization algorithms. Positive definite systems. Indefinite systems. Gaussian elimination for H-matrices. Block methods. Tridiagonal and block tridiagonal systems. Roundoff error analysis. Perturbation analysis. Scaling. Iterative refinement. Parallel solution of general linear systems. Bibliographical comments.

Details

No. of pages:
776
Language:
English
Copyright:
© 1999
Published:
Imprint:
North Holland
Print ISBN:
9780444501691
Electronic ISBN:
9780080529516