Rounding Errors in Algebraic Processes

[This book] combines a rigorous mathematical analysis with a practicality that stems from an obvious first-hand contact with the actual numerical computation. The well-chosen examples alone show vividly both the importance of the study of rounding errors and the perils of its neglect." A. A. Grau, SIAM Review (1966) Rounding Errors in Algebraic Processes was the first book to give systematic analyses of the effects of rounding errors on a variety of key computations involving polynomials and matrices. A detailed analysis is given of the rounding errors made in the elementary arithmetic operations and inner products, for both floating-point arithmetic and fixed-point arithmetic. The results are then applied in the error analyses of a variety of computations involving polynomials as well as the solution of linear systems, matrix inversion, and eigenvalue computations. The conditioning of these problems is investigated. The aim was to provide a unified method of treatment, and emphasis is placed on the underlying concepts.

James Hardy Wilkinson (1919--1986) was a pioneer in numerical analysis. He graduated in pure mathematics from Trinity College, Cambridge in 1939 and was then drafted into military work with the British Government Ministry of Supply. After World War II ended, he joined Alan Turing at the UK National Physical Laboratory, where he remained his entire career. By 1974 he had become a Special Merit Chief Scientific Officer, a rare appointment. He was elected to the Royal Society in 1969, and in 1970 received both the A. M. Turing award from the Association of Computing Machinery and the John von Neumann award from SIAM. Other honors include being elected Distinguished Fellow of the British Computer Society in 1974 and the MAA Chauvenet Prize in 1987. Argonne National Laboratory has a Wilkinson Postdoctoral Fellowship in Scientific Computing for early career scientists, and SIAM has two prizes that recognize Wilkinson's contributions: the James H. Wilkinson Prize for Numerical Software and the James H. Wilkinson Prize in Numerical Analysis and Scientific Computing, both intended to encourage early career researchers.