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Introduction to matrix computations
Rounding-Error Analysis of Solution of Triangular Systems and of Gaussian Elimination.
An Algorithm for Generalized Matrix Eigenvalue Problems.
A new method, called the $QZ$ algorithm, is presented for the solution of the matrix eigenvalue problem $Ax = \lambda Bx$ with general square matrices A and B. Particular attention is paid to the
Error and Perturbation Bounds for Subspaces Associated with Certain Eigenvalue Problems
This paper describes a technique for obtaining error bounds for certain characteristic subspaces associated with the algebraic eigenvalue problem, the generalized eigenvalue problem, and the singular
Solution of the matrix equation AX + XB = C [F4]
The algorithm is supplied as one file of BCD 80 character card images at 556 B.P.I., even parity, on seven ~rack tape, and the user sends a small tape (wt. less than 1 lb.) the algorithm will be copied on it and returned to him at a charge of $10.O0 (U.S.and Canada) or $18.00 (elsewhere).
Matrix algorithms
This volume treats the numerical solution of dense and large-scale eigenvalue problems with an emphasis on algorithms and the theoretical background required to understand them.
A Krylov-Schur Algorithm for Large Eigenproblems
  • G. Stewart
  • Computer Science
    SIAM J. Matrix Anal. Appl.
  • 1 March 2001
A general Krylov decomposition is introduced that solves both the problem of deflate converged Ritz vectors and the potential forward instability of the implicit QR algorithm in a natural and efficient manner.
Reorthogonalization and stable algorithms for updating the Gram-Schmidt QR factorization
Numerically stable algorithms are given for updating the GramSchmidt QR factorization of an m X n matrix A (m > n) when A is modified by a matrix of rank one, or when a row or column is inserted or
On the Early History of the Singular Value Decomposition
This paper surveys the contributions of five mathematicians who were responsible for establishing the existence of the singular value decomposition and developing its theory.