Have you ever tried Julia?

What do you think about it?

— Cleve ]]>

Summary, paragraph 2: “Multiplication” should be Multiprecision (in reference to Advanpix).

]]>It is a pleasure to read your new post in which you look back to classic subjects (and to the very important work of Walter Gautschi). With your reference to chapter 22 of your book you are implicitly remembering your milestone paper of 1987 on the error analysis of Björck-Pereyra algorithms for Vandermonde systems, which you extended (the analysis and the algorithms) in your book.

I would like to remark the important role of the total positivity of the Vandermonde matrix (if positive nodes are increasingly ordered), which implies the inverse matrix has a checkerboard sign pattern. These facts are briefly recalled in the recent book of Björck “Numerical Methods in Matrix Computations”.

Unfortunately, so many years after your work (and the work of Boros, Kailath and Olshevsky for Cauchy matrices, and of Demmel and Koev for general totally nonnegative matrices) we still must sadly read (for example in a recent paper on interpolation by Mark Ainsworth and Manuel A. Sánchez) that “the interplay between the ideas of total positivity and Neville elimination are not part of the standard armory of many nonspecialists”. So I would be glad to read in the future some detailed comment from you on these subjects (extending your sentence “appropriate algorithms that exploit structure can nevertheless obtain accurate solutions”), which from my humble point of view should already be basic facts in the numerical linear algebra field.

Thank you very much for your work.

Thanks to your review in this post, I discovered (and subsequently bought) this wonderful book last summer. It has been very useful to me in the design of an “ideal” subject I have called Linear Algebra II, an extension of the “real” subject I am teaching: Linear Algebra.

I do not know if that ideal subject will become real in the future (the third course you cite is certainly science fiction in my engineering teaching), but in the meantime the book has been of great help in my study of this field in connection with teaching.

Thank you very much for your work.

]]>It seems that the correct word is Palomino.

Thank you for your work. ]]>