Quotes on Accuracy and Stability of Numerical Algorithms

by Nicholas J. Higham

"A superb book by a leading scientist and scholar. It will be the definitive work on error analysis for years to come."
-- G. W. Stewart, University of Maryland


"This is a masterful book. Primarily it studies the influence of roundoff errors on algorithms to solve dense linear systems of equations and least squares problems...What Higham has done, both in his research and in this book, is to revisit all this material in his own way and unearth gaps and weaknesses that none of us suspected. With characteristic thoroughness Higham has read, and digested, almost all that has been published on his chosen topics from the beginning. He has crafted his notation with care and we will all benefit from his scholarship, his powers of exposition, and his quotations."
-- Beresford Parlett, University of California, Berkeley


"Nick Higham, already famous for his writing abilities, has produced the next "bible" of accuracy and stability. Finally, a modern book properly demonstrates the art and science of analyzing rounding errors. With over 1,100 references, Higham's book is the most comprehensive and scholarly treatment of the field. This book may be used as a classroom text, as a reference for current and future designers of numerical software libraries, or for anyone who simply may have wondered whether the order of summation of floating point numbers matters or whether the condition number is all there is to understand about the "goodness" in a matrix. The book is a pleasure to read, the problems are wonderful, and most importantly Higham includes terrific open research problems. I wonder how many will have been solved by the year 2100."
-- Alan Edelman, Massachusetts Institute of Technology


"This book is a monumental work on the analysis of rounding error, and will serve as a new standard textbook on this subject, especially for linear computation."
-- S. Hitotumatu, Math. Reviews, 97a:65047


"The well-known book by J. Wilkinson appeared in 1963 and it was a reference since then. I am quite sure that the book by Nick Higham will play the same role in the future."
-- Claude Brezinski, Numerical Algorithms 13(1/2), 1996


"This text may become the new `Bible' about accuracy and stability for the solution of systems of linear equations. It covers 688 pages carefully collected, investigated, and written, dedicated to two pioneers in this field, Alan M. Turing and James H. Wilkinson."
-- N. Kockler, Zbl. Math. 847


"The main role that the book will assume in the coming years will be as a reference and as a companion text in the classroom. Wilkinson's Algebraic Eigenvalue Problem played a similar role in the 1970s and 1980s and I bet Higham's book will prove to be equally valuable in the long run. ... The volume is laced with great quotations and my favorite is due to Beresford Parlett:

One of the major difficulties in a practical [error] analysis is that of description. An ounce of analysis follows a pound of preparation.
No numerical analyst can change that ratio. With tons of preparation Higham has given us a hundred-weight of analysis---enough to keep the field on solid foundations for years to come."
-- Charles Van Loan, Math. Comp. 66(220), 1997.


"This definitive source on the accuracy and stability of numerical algorithms is quite a bargain and a worthwhile addition to the library of any statistician heavily involved in computing."
-- Robert L. Strawderman, Journal of the American Statistical Association, March 1999.


"Nick Higham has assembled an enormous amount of important and useful material in a coherent, readable form. His book belongs on the shelf of anyone who has more than a casual interest in rounding error and matrix computations. I hope the author will give us the 600-odd hundred page sequel. But if not, he has more than earned his respite--and our gratitude."
-- G. W. Stewart, SIAM Review, March 1997.


"A valuable reference and sourcebook for numerical analysis."
-- Thomas Kailath, Ali H. Sayed and Babak Hassibi, Linear Estimation, Prentice-Hall, 2000 (p. 452).


"You have to learn the techniques of error analysis and decide what degree of error is tolerable. There are three good books: Accuracy and Stability of Numerical Algorithms, by Nicholas J. Higham, ..., Matrix Computations, Third Edition, by Gene H. Golub and Charles F. Van Loan, ... and The Algebraic Eigenvalue Problem, by J. H. Wilkinson."
-- A Conversation with William Kahan, Dr. Dobb's Journal, 271, pp. 18-32, 1997.


"After its publication in 1996, the first edition quickly became the premier reference for the stability and error analysis of numerical algorithms... But this book is far more than a research monograph. Higham framed the results with their historical context and practical implications... In short, Accuracy and Stability of Numerical Algorithms belongs in the library of anyone with an interest in numerical linear algebra.
-- Donald Estep, SIAM Review, 46(1), 2004.