[DJVU] [1991] Biorthogonality and its Applications to Numerical torrent

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BOOK INFO:

Biorthogonality and its Applications to Numerical Analysis (Pure and Applied Mathematics)
By Claude Brezinski


Publisher: CRC
Number Of Pages: 184
Publication Date: 1991-11-27
ISBN-10 / ASIN: 0824786165
ISBN-13 / EAN: 9780824786168
Binding: Hardcover


Preface:

The solution of the general interpolation problem has very many applications in numerical analysis and applied mathematics. However, some time ago, I realized that its possibilities have not been fully exploited and have even been underestimated, and I began to work on the subject. The concept underlying the problem is that of biorthogonality which gave its title to this book. It has many unusual connections and applications to Fourier expansion, projections, divided differences, extrapolation processes, numerical methods for integrating differential equations or for solving integral equations, rational approximations to formal power series and series of functions, least squares, statistics, and biorthogonal polynomials, to name some. Most of the results given in this book are new and have not even been published in the form of journal articles. They appear here for the first time. This is the case in particular for the various recurrence relations given and for the generalizations of the method of moments, the method of Lanczos, and the biconjugate gradient method. New approximations of Pade-type for series are also described. The possibilities opened by the concept of biorthogonality have still to be discovered and new applications as well. Thus, this book will be of interest to researchers in numerical analysis and approximation theory. However, this does not mean that the material given here is difficult. Almost no prerequisite are needed and the book can also be used as a text for students. I hope that this monograph will be useful to many applied mathematicians and will serve as a basis for new developments and applications. I would like to thank Professor Zuhair Nashed and Professor Earl Taft, who accepted the book in their series. I express my gratitude to Professor Jet Wimp for his encouragement during the preparation of the manuscript. My thanks are also due to Mrs. Francoise Tailly who carefully typed the manuscript, and Ms. Maria Allegra of Marcel Dekker, Inc., for their assistance in the production of the book. CLAUDE BREZINSKI