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… Expand

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… Expand

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).Expand

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.Expand

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.Expand

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… Expand

This paper surveys the contributions of five mathematicians who were responsible for establishing the existence of the singular value decomposition and developing its theory.Expand