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Some History of the Conjugate Gradient and Lanczos Algorithms: 1948-1976
Some History of the Conjugate Gradient and Lanczos Algorithms: 1948-1976 Gene H. Golub; Dianne P. O'Leary SIAM Review, Vol. 31, No. 1. (Mar., 1989), pp. 50-102. Stable URL: http://links.jstor.org/sici?sici=0036-1445%28198903%2931%3A1%3C50%3ASHOTCG%3E2.0.CO%3B2-S SIAM Review is currently published by Society for Industrial and Applied Mathematics. Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at http://www.jstor.org/about/terms.html. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use. Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at http://www.jstor.org/journals/siam.html. Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed page of such transmission. The JSTOR Archive is a trusted digital repository providing for long-term preservation and access to leading academic journals and scholarly literature from around the world. The Archive is supported by libraries, scholarly societies, publishers, and foundations. It is an initiative of JSTOR, a not-for-profit organization with a mission to help the scholarly community take advantage of advances in technology. For more information regarding JSTOR, please contact [email protected]. http://www.jstor.org Fri Aug 17 11:22:18 2007 SIAM REVIEW 0 1989 Society for Industrial and Applied Mathematics Vol. -
REVIEWS and DESCRIPTIONS of TABLES and BOOKS the Numbers
MATHEMATICS OF COMPUTATION Volume 65, Number 213, January 1996, Pages 429{443 S 0025-5718-96-00698-9 REVIEWS AND DESCRIPTIONS OF TABLES AND BOOKS The numbers in brackets are assigned according to the American Mathematical Society classification scheme. The 1991 Mathematics Subject Classification can be found in the annual subject index of Mathematical Reviews starting with the December 1990 issue. 1[65-00, 41-00, 41A05, 41A21, 41A55, 41A65, 65C05, 65H05, 65T20, 73C50, 73V20]—Handbook of numerical analysis, Vol. III, P. G. Ciarlet and J. L. Lions (Editors), Techniques of scientific computing (Part 1), Numerical methods for solids (Part 1), Solution of equations in Rn (Part 2), North-Holland, 1 Amsterdam, 1994, x+778 pp., 24 2 cm, $154.25/Dfl. 270.00 This book contains three parts: 1) Techniques of Scientific Computing; 2) Nu- merical Methods for Solids; 3) Solution of Equations in Rn. Nevertheless, only the second part gets close to “numerical methods for large-scale computation”. The aims of the book are rather “constructive methods”, which are often the background to numerical methods. The first part is concerned with three aspects of approximation theory. First, Claude Brezinski provides an interesting historical perspective on interpolation, ap- proximation and numerical quadrature since the year 1611. His main contribution, however, is a survey on Pad´e approximation, written jointly with van Iseghen. The algebraic theory naturally elucidates the connections with orthogonal polynomi- als and continued fractions. The convergence theory contains, on the one hand, a complete theory for Stieltjes functions and, on the other hand, only convergence in capacity for the general case. -
German Jews in the United States: a Guide to Archival Collections
GERMAN HISTORICAL INSTITUTE,WASHINGTON,DC REFERENCE GUIDE 24 GERMAN JEWS IN THE UNITED STATES: AGUIDE TO ARCHIVAL COLLECTIONS Contents INTRODUCTION &ACKNOWLEDGMENTS 1 ABOUT THE EDITOR 6 ARCHIVAL COLLECTIONS (arranged alphabetically by state and then city) ALABAMA Montgomery 1. Alabama Department of Archives and History ................................ 7 ARIZONA Phoenix 2. Arizona Jewish Historical Society ........................................................ 8 ARKANSAS Little Rock 3. Arkansas History Commission and State Archives .......................... 9 CALIFORNIA Berkeley 4. University of California, Berkeley: Bancroft Library, Archives .................................................................................................. 10 5. Judah L. Mages Museum: Western Jewish History Center ........... 14 Beverly Hills 6. Acad. of Motion Picture Arts and Sciences: Margaret Herrick Library, Special Coll. ............................................................................ 16 Davis 7. University of California at Davis: Shields Library, Special Collections and Archives ..................................................................... 16 Long Beach 8. California State Library, Long Beach: Special Collections ............. 17 Los Angeles 9. John F. Kennedy Memorial Library: Special Collections ...............18 10. UCLA Film and Television Archive .................................................. 18 11. USC: Doheny Memorial Library, Lion Feuchtwanger Archive ................................................................................................... -
ITS FIRST FIFTY YEARS Carl Β
THE MATHEMATICAL ASSOCIATION OF AMERICA: ITS FIRST FIFTY YEARS Carl Β. Boyer Brooklyn College, CUNY Richard W. Feldmann Lycoming College Harry M. Gehman SUN Yat Buffalo Phillip S. Jones University of Michigan Kenneth O. May University of Toronto Harriet F. Montague SUNYat Buffalo Gregory H. Moore University of Toronto Robert A. Rosenbaum Wesleyan University Emory P. Starke Rutgers University Dirk J. Struik Massachusetts Institute of Technology THE MATHEMATICAL ASSOCIATION OF AMERICA: ITS FIRST FIFTY YEARS Kenneth O. May, editor University of Toronto, Canada Published and distributed by The Mathematical Association of America Copyright 1972 by THE MATHEMATICAL ASSOCIATION OF AMERICA (INCORPORATED) PREFACE The fiftieth anniversary of the founding of the Mathematical Association of America was celebrated at the 1965 summer meeting at Cornell University [MONTHLY 72, 1053-1059]. The invited addresses on that occasion dealing with the past, present, and future of the Association and of mathematics, were published in the fiftieth anniversary issue [MONTHLY 74, Num. !, Part II] under the editorship of Carl B. Allendoerfer. The historical addresses by A. A. Bennett, R. A. Rosenbaum, W. L. Duren, Jr., and P. S. Jones whetted appetites for a more complete story of the Association. Early in 1966, on a recommendation of the Committee on Publications, President R. L. Wilder appointed a Committee on the Preparation of a Fifty-Year History of the Association consisting of Carl B. Boyer, Kenneth O. May (Chairman), and Dirk J. Struik. An appropriation of one thousand dollars was set aside to meet incidental expenses. The Committee began its work with very ambitious plans, hoping to get financial support for interviewing older members of the Association and the preparation of special studies on particular aspects of the Association's work. -
Notices of the American Mathematical
OF THE AMERICAN MATHEMATICAL SOCIETY VOLUMf 12, NUMBER 2 ISSUE NO. 80 FEBRUARY 1965 cNotiaiJ OF THE AMERICAN MATHEMATICAL SOCIETY Edited by John W. Green and Gordon L. \Yalker CONTENTS MEETINGS Calendar of Meetings o o o o o o o o o • o o • o o o o o o o • o 0 o 0 o 0 • 0 • 0 0 • 0 0 184 Program of the Meeting in New York. o 0 o 0 o 0 0 • 0 o o o 0 0 0 0 • 0 0 0 0 0 • 185 Abstracts for the Meeting- Pages 209-216 PRELIMINARY ANNOUNCEMENTS OF MEETINGS • o o o o o o o o • o 0 • 0 • 0 • • • 188 ACTIVITIES OF OTHER ASSOCIATIONS •••• o o. o o o o • o o o •• o 0 0 0. o 0 0 0 0 191 LETTERS TO THE EDITOR • o ••••• o o • o o o o o • o ••• o •••• o o o •• o o • o o 192 MEMORANDA TO MEMBERS List of Retired Mathematicians 190 Increase in Page Charges o o ••• o •• o • o o o •••••• 0 ••• 0 0 0 •• 0 0 0 0 194 Journals in Microform • o •••• o 0 ••• o • o ••• 0 •• o ••••• 0 •• 0 • • • • 194 Backlog of Mathematics Research Journals 0 0 0. 0. 0 ••• 0 •• 0 •• 0.. 195 Corporate Members ••••••••••••• 0 • 0 0 0 0 •• 0 0 • 0 •• 0 0 •• 0 ••• 0 201 ASSISTANTSHIPS AND FELLOWSHIPS IN MATHEMATICS 1965-1966 0 ••• 0 • 0 196 NEW AMS PUBLICATIONS • o •• o •• o •••• o • o o ••••• o o o •• o o •• o • o • o • 197 PERSONAL ITEMS .••••• o •• o. -
Winter 2013 Newsletter
Volume 10, No. 1 Newsletter The Courant Institute of Mathematical Sciences at New York University 2013 Winter 2 Jinyang Li: Building 5 How can the mysterious Distributed Systems that connection between Bridge Applications and nature and mathematics Hardware be explained? It can’t, says Henry McKean 3 New Faculty 6 Winter 2013 Puzzle How Fair is a Fair Coin? 4 In the accounting software 7 The Generosity of Friends field, Anne-Claire McAllister’s Courant degree has made all the difference In this Issue: Jinyang Li: Building Distributed Systems That Bridge Applications and Hardware by M.L. Ball the hardware. When new hardware is built, without good systems Piccolo: Distributed Computation software it’s very clumsy to use and won’t reach the majority of using Shared In-memory State application programmers. It’s a careful balance between making your system very usable and maintaining extremely high performance,” Node-1 said Jinyang. Get, Put, Update (commutative) Jinyang’s Project Piccolo: Faster, more robust, and getting lots of notice When approaching a new project, Jinyang prefers a bottom-up PageRank Accumulate=sum Distrubuted in-memory state approach. “I like to take a very concrete piece of application that A: 1.35 B: 5.44 I really care about – like machine learning or processing a lot of C: 2.01 … text – and then look at the existing hardware and say, ‘We have lots of machines and they’re connected by a fast network and each of them has a lot of memory and a lot of disks,’” she said. “‘How can I enable that application to utilize this array of hardware? What is the Node-2 Node-3 glue, what is the infrastructure that’s needed? To make the challenges concrete, let me start by building this infrastructure that specifically can process a large amount of text really quickly. -
Selected Papers
Selected Papers Volume I Arizona, 1968 Peter D. Lax Selected Papers Volume I Edited by Peter Sarnak and Andrew Majda Peter D. Lax Courant Institute New York, NY 10012 USA Mathematics Subject Classification (2000): 11Dxx, 35-xx, 37Kxx, 58J50, 65-xx, 70Hxx, 81Uxx Library of Congress Cataloging-in-Publication Data Lax, Peter D. [Papers. Selections] Selected papers / Peter Lax ; edited by Peter Sarnak and Andrew Majda. p. cm. Includes bibliographical references and index. ISBN 0-387-22925-6 (v. 1 : alk paper) — ISBN 0-387-22926-4 (v. 2 : alk. paper) 1. Mathematics—United States. 2. Mathematics—Study and teaching—United States. 3. Lax, Peter D. 4. Mathematicians—United States. I. Sarnak, Peter. II. Majda, Andrew, 1949- III. Title. QA3.L2642 2004 510—dc22 2004056450 ISBN 0-387-22925-6 Printed on acid-free paper. © 2005 Springer Science+Business Media, Inc. All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, Inc., 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed in the United States of America. -
Implications for Understanding the Role of Affect in Mathematical Thinking
Mathematicians and music: Implications for understanding the role of affect in mathematical thinking Rena E. Gelb Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy under the Executive Committee of the Graduate School of Arts and Sciences COLUMBIA UNIVERSITY 2021 © 2021 Rena E. Gelb All Rights Reserved Abstract Mathematicians and music: Implications for understanding the role of affect in mathematical thinking Rena E. Gelb The study examines the role of music in the lives and work of 20th century mathematicians within the framework of understanding the contribution of affect to mathematical thinking. The current study focuses on understanding affect and mathematical identity in the contexts of the personal, familial, communal and artistic domains, with a particular focus on musical communities. The study draws on published and archival documents and uses a multiple case study approach in analyzing six mathematicians. The study applies the constant comparative method to identify common themes across cases. The study finds that the ways the subjects are involved in music is personal, familial, communal and social, connecting them to communities of other mathematicians. The results further show that the subjects connect their involvement in music with their mathematical practices through 1) characterizing the mathematician as an artist and mathematics as an art, in particular the art of music; 2) prioritizing aesthetic criteria in their practices of mathematics; and 3) comparing themselves and other mathematicians to musicians. The results show that there is a close connection between subjects’ mathematical and musical identities. I identify eight affective elements that mathematicians display in their work in mathematics, and propose an organization of these affective elements around a view of mathematics as an art, with a particular focus on the art of music. -
RM Calendar 2017
Rudi Mathematici x3 – 6’135x2 + 12’545’291 x – 8’550’637’845 = 0 www.rudimathematici.com 1 S (1803) Guglielmo Libri Carucci dalla Sommaja RM132 (1878) Agner Krarup Erlang Rudi Mathematici (1894) Satyendranath Bose RM168 (1912) Boris Gnedenko 1 2 M (1822) Rudolf Julius Emmanuel Clausius (1905) Lev Genrichovich Shnirelman (1938) Anatoly Samoilenko 3 T (1917) Yuri Alexeievich Mitropolsky January 4 W (1643) Isaac Newton RM071 5 T (1723) Nicole-Reine Etable de Labrière Lepaute (1838) Marie Ennemond Camille Jordan Putnam 2002, A1 (1871) Federigo Enriques RM084 Let k be a fixed positive integer. The n-th derivative of (1871) Gino Fano k k n+1 1/( x −1) has the form P n(x)/(x −1) where P n(x) is a 6 F (1807) Jozeph Mitza Petzval polynomial. Find P n(1). (1841) Rudolf Sturm 7 S (1871) Felix Edouard Justin Emile Borel A college football coach walked into the locker room (1907) Raymond Edward Alan Christopher Paley before a big game, looked at his star quarterback, and 8 S (1888) Richard Courant RM156 said, “You’re academically ineligible because you failed (1924) Paul Moritz Cohn your math mid-term. But we really need you today. I (1942) Stephen William Hawking talked to your math professor, and he said that if you 2 9 M (1864) Vladimir Adreievich Steklov can answer just one question correctly, then you can (1915) Mollie Orshansky play today. So, pay attention. I really need you to 10 T (1875) Issai Schur concentrate on the question I’m about to ask you.” (1905) Ruth Moufang “Okay, coach,” the player agreed. -
Matical Society Was Held at Columbia University on Friday and Saturday, April 25-26, 1947
THE APRIL MEETING IN NEW YORK The four hundred twenty-fourth meeting of the American Mathe matical Society was held at Columbia University on Friday and Saturday, April 25-26, 1947. The attendance was over 300, includ ing the following 300 members of the Society: C. R. Adams, C. F. Adler, R. P. Agnew, E.J. Akutowicz, Leonidas Alaoglu, T. W. Anderson, C. B. Allendoerfer, R. G. Archibald, L. A. Aroian, M. C. Ayer, R. A. Bari, Joshua Barlaz, P. T. Bateman, G. E. Bates, M. F. Becker, E. G. Begle, Richard Bellman, Stefan Bergman, Arthur Bernstein, Felix Bernstein, Lipman Bers, D. H. Blackwell, Gertrude Blanch, J. H. Blau, R. P. Boas, H. W. Bode, G. L. Bolton, Samuel Borofsky, J. M. Boyer, A. D. Bradley, H. W. Brinkmann, Paul Brock, A. B. Brown, G. W. Brown, R. H. Brown, E. F. Buck, R. C. Buck, L. H. Bunyan, R. S. Burington, J. C. Burkill, Herbert Busemann, K. A. Bush, Hobart Bushey, J. H. Bushey, K. E. Butcher, Albert Cahn, S. S. Cairns, W. R. Callahan, H. H. Campaigne, K. Chandrasekharan, J. O. Chellevold, Herman Chernoff, Claude Chevalley, Ed mund Churchill, J. A. Clarkson, M. D. Clement, R. M. Cohn, I. S. Cohen, Nancy Cole, T. F. Cope, Richard Courant, M. J. Cox, F. G. Critchlow, H. B. Curry, J. H. Curtiss, M. D. Darkow, A. S. Day, S. P. Diliberto, J. L. Doob, C. H. Dowker, Y. N. Dowker, William H. Durf ee, Churchill Eisenhart, Benjamin Epstein, Ky Fan, J.M.Feld, William Feller, F. G. Fender, A. D. -
Fundamental Theorems in Mathematics
SOME FUNDAMENTAL THEOREMS IN MATHEMATICS OLIVER KNILL Abstract. An expository hitchhikers guide to some theorems in mathematics. Criteria for the current list of 243 theorems are whether the result can be formulated elegantly, whether it is beautiful or useful and whether it could serve as a guide [6] without leading to panic. The order is not a ranking but ordered along a time-line when things were writ- ten down. Since [556] stated “a mathematical theorem only becomes beautiful if presented as a crown jewel within a context" we try sometimes to give some context. Of course, any such list of theorems is a matter of personal preferences, taste and limitations. The num- ber of theorems is arbitrary, the initial obvious goal was 42 but that number got eventually surpassed as it is hard to stop, once started. As a compensation, there are 42 “tweetable" theorems with included proofs. More comments on the choice of the theorems is included in an epilogue. For literature on general mathematics, see [193, 189, 29, 235, 254, 619, 412, 138], for history [217, 625, 376, 73, 46, 208, 379, 365, 690, 113, 618, 79, 259, 341], for popular, beautiful or elegant things [12, 529, 201, 182, 17, 672, 673, 44, 204, 190, 245, 446, 616, 303, 201, 2, 127, 146, 128, 502, 261, 172]. For comprehensive overviews in large parts of math- ematics, [74, 165, 166, 51, 593] or predictions on developments [47]. For reflections about mathematics in general [145, 455, 45, 306, 439, 99, 561]. Encyclopedic source examples are [188, 705, 670, 102, 192, 152, 221, 191, 111, 635]. -
Methods of Conjugate Gradients for Solving Linear Systems
Methods of Conjugate Gradients for Solving Linear Systems The advent of electronic computers in the middle of systematic way in order to compute the solution. These the 20th century stimulated a flurry of activity in devel- methods were finite, but required a rather large amount oping numerical algorithms that could be applied to of computational effort with work growing as the cube computational problems much more difficult than those of the number of unknowns. The second type of al- solved in the past. The work described in this paper [1] gorithm used “relaxation techniques” to develop a se- was done at the Institute for Numerical Analysis, a quence of iterates converging to the solution. Although part of NBS on the campus of UCLA [2]. This institute convergence was often slow, these algorithms could be was an incredibly fertile environment for the develop- terminated, often with a reasonably accurate solution ment of algorithms that might exploit the potential estimate, whenever the human “computers” ran out of of these new automatic computing engines, especially time. algorithms for the solution of linear systems and matrix The ideal algorithm would be one that had finite eigenvalue problems. Some of these algorithms are termination but, if stopped early, would give a useful classified today under the term Krylov Subspace approximate solution. Hestenes and Stiefel succeeded in Iteration, and this paper describes the first of these developing an algorithm with exactly these characteris- methods to solve linear systems. tics, the method of conjugate gradients. Magnus Hestenes was a faculty member at UCLA The algorithm itself is beautiful, with deep connec- who became associated with this Institute, and Eduard tions to optimization theory, the Pad table, and quadratic Stiefel was a visitor from the Eidgeno¨ssischen Technis- forms.