Author's reply to the review of Introduction to Numerical Linear Algebra and Optimisation (P. G. Ciarlet)

I was startled by the review that John C. Nash (University of Ottawa) has made of my book Introduction to Numerical LinearAlgebra and Optimisation in SlAMReview [1]. The declared objective of this book ("to give a thorough description, and a rigorous mathematical analysis, of some of the most commonly used methods in Numerical Linear Algebra and Optimisation") is only discussed in very general terms by the reviewer, who makes only cursory, sometimes surprising, and in two cases erroneous1, comments on this objective. In what occupies exactly half of his review, the reviewer then unjustly concentrates his complaints on software issues, giving the erroneous impression that this book is one on software, whereas it is obviously one that addresses mathematical issues. I of course am perfectly aware of the interest of providing the reader with some information on sources of good available software and I certainly intend to do so in future editions. But in my opinion, it should not exceed several pages in this kind ofbook, as exemplified by Appendix C: "Computer Codes for Linear Algebra" (11 pages) in Gilbert Strang’s admirable book: Linear Algebra and Its Applications [2]. I was also annoyed at the inferences ("possibly under marketing pressure from the publishers") that Cambridge University Press had persuaded me to "oversell the work", or that it is not me alone who prepared a "reasonable index." Finally, the reviewer fails to mention that the original French edition, of which this book is a translation, appeared in 1982, even though this fact is explicitly mentioned, page iv. This being the case, how could any information posterior to 1982 have been possibly taken into account? (In fact, the actual writing was completed in December 1980, as indicated in the Preface of the French original edition.) I am very concerned that this review will durably hurt the "image" of this book, which has otherwise been very well received so far: To date, more than 8,000 copies of the French edition have been sold; Cambridge University Press hasjust reprinted the softcover edition; It has already been translated in English (Cambridge University Press, 1989; this is the book under review), into Italian (Masson Italia, 1989), into Chinese (Central Chinese Publishing House, 1990); it is currently being translated into Japanese. All the other reviewers of this book that know of are of a different tone; see, for instance, Computing Reviews, (1990), pp. 138139; ibid, June 1990, p. 296; Journal ofApplied Mathematical Physics, 41, (1990).