Numerical Linear Algebra: Twenty-Fifth Anniversary Edition
Since its original appearance in 1997, Numerical Linear Algebra has been a leading textbook in its field, used in universities around the world. It is noted for its 40 lecture-sized short chapters and its clear and inviting style. It is reissued here with a new foreword by James Nagy and a new afterword by Yuji Nakatsukasa about subsequent developments.
The Arnoldi Iteration
The Lanczos Iteration
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accuracy algorithm analysis applied approximation arithmetic Arnoldi backward coefficients columns computed condition number consider convergence corresponding count defined definite described determined diagonal dimension direct discussed eigenvalues eigenvectors entries equal equations errors example Exercise fact Figure floating point flops formula function Gaussian elimination give given GMRES hermitian Householder idea introduced inverse involving iteration known Lanczos least squares problem Lecture machine mathematical matrix means methods multiplication norm normal Note numerical numerical linear algebra obtain operations orthogonal orthogonal matrix perturbations pivoting polynomial positive practice problem Proof QR algorithm QR factorization random rank reduced requires result satisfying Show SIAM singular values solution solve space stability standard step Suppose symmetric symmetric matrix Theorem triangular tridiagonal unitary vector Write zeros