The Algebraic Eigenvalue Problem
"Since the advent of computers, a very large number of algorithms have been proposed for the solution of the algebraic eigenvalue problem. In this classic book which was first published in 1965, the author explores the relationship between these algorithms and gives a critical assessment of them based on rigorous error analyses. In order to give deeper insight into the factors which determine numerical stability, descriptions of both stable and unstable algorithms are included. The algorithms are presented in terms which are closely related to those used in programming languages. Two related problems, the solution of linear equations and the calculation of zeros of polynomials, are also covered and the techniques of error analysis which are developed are applicable to a wide range of computations." --Back cover.
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B. N. Parlett's review of this work, in "SIAM Review" (Vol. 8, No. 4 (Oct., 1966), pp. 543-545) expresses the value of this book far better than I can. My only complaint about this book is for the publisher, not for the author (rest his soul!): Keeping Wilkinson's works so expensive is a crime against mathematics!