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MATHEMATICAL FOUNDATIONS OF HIGH-PERFORMANCE COMPUTING AND COMMUNICATIONS Pane' on the Mathematical Sciences in High-Performance Computing and Communications Board on Mathematical Sciences Commission on Physical Sciences, Mathematics, and Applications National Research Council National Academy Press Washington, D.C. 1991

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NOTICE: The project that is the subject of this report was approved by the Governing Board of the National Research Council, whose members are drawn from the councils of the National Academy of Sciences, the National Academy of Engineering, and the Institute of Medicine. The National Academy of Sciences is a private, nonprofit, self-perpetuating society of distinguished scholars engaged in scientific and engineering research, dedicated to the furtherance of science and technology and to their use for the general welfare. Upon the authority of the charter granted to it by the Congress in 1863, the Academy has a mandate that requires it to advise the federal government on scientific and technical matters. Dr. Frank Press is president of the National Academy of Sciences. The National Academy of Engineering was established in 1964, under the charter of the National Academy of Sciences, as a parallel organization of outstanding engineers. It is autonomous in its administration and in the selection of its members, sharing with the National Academy of Sciences the responsibility for advising the federal government. The National Academy of Engineering also sponsors engineering programs aimed at meeting national needs, encourages education and research, and recognizes the superior achievement of engineers. Dr. Robert M. White is president of the National Academy of Engineering. The Institute of Medicine was established in 1970 by the National Academy of Sciences to secure the services of eminent members of appropriate professions in the examination of policy matters pertaining to the health of the public. The Institute acts under the responsibility given to the National Academy of Sciences by its congressional charter to be an adviser to the federal government and, upon its own initiative, to identify issues of medical care, research, and education. Dr. Stuart Bondurant is acting president of the Institute of Medicine. The National Research Council was organized by the National Academy of Sciences in 1916 to associate the broad community of science and technology with the Academy's purposes of furthering knowledge and advising the federal government. Functioning in accordance with general policies determined by the Academy, the Council has become the principal operating agency of both the National Academy of Sciences and the National Academy of Engineering in providing services to the government, the public, and the scientific and engineering communities. The Council is administered jointly by both Academies and the Institute of Medicine. Dr. Frank Press and Dr. Robert M. White are chairman and vice chairman, respectively, of the National Research Council. The National Research Council established the Board on Mathematical Sciences in 1984. The objectives of the Board are to maintain awareness and active concern for the health of the mathematical sciences and to serve as the focal point in the National Research Council for issues connected with the mathematical sciences. In addition, the Board is designed to conduct studies for federal agencies and maintain liaison with the mathematical sciences communities and academia, professional societies, and industry. Support for this project was provided by the National Science Foundation. Available from: Board on Mathematical Sciences National Research Council 2101 Constitution Avenue, N.W. Washington, D.C. 20418 (202) 334-2421 Printed in the United States of America

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PANEL ON THE MATHEMATICAL SCIENCES IN HIGH-PERFORMANCE COMPUTING AND COMMUNICATIONS AVNER FRIEDMAN, University of Minnesota, Chair LOUIS AUSLANDER, City University of New York RANDOLPH E. BANK, University of California at San Diego RICHARD E. EWING, University of Wyoming JAMES L`. FLANAGAN, Rutgers University STUART A. GEMAN, Brown University JAMES M. HYMEN, Los Amos National Laboratory JOHN P. LEHOCZKY, Carnegie Mellon University CECIL E. LEITH, JR., Lawrence Livermore Laboratory JILL P. MESIROV, Thinking Machines Corporation GEORGE C. PAPANICOLAOU, New York University GEORGE R. SELL, University of Minnesota PETER I. WEINBERGER, AT&T Bell Laboratories Staff Scorr T. WEIDMAN, Senior Staff Officer -

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BOARD ON MATHEMATICAL SCIENCES SHMUEL WINOGRAD, IBM TV. Watson Research Center, Chair RONALD DOUGLAS, State University of New York-Stony Brook, ~ce-Chair LAWRENCE D. BROWN, Cornell University SUN YUNG A. CHANG, University of California at Los Angeles JOEL E. COHEN, Rockefeller University AVNER FRIEDMAN, University of Minnesota JOHN F. GEWEKE, University of Minnesota JAMES GLIMM, State University of New York-Stony Brook PHILLIP A. GRIFFITHS, Institute for Advanced Study DIANE LAMBERT, AT&T Bell Laboratories GERALD I. LIEBERMAN, Stanford University RONALD F. PEIERLS, Brookhaven National Laboratory JEROME SACKS, National Institute of Statistical Sciences Ex Officio Member WILLIAM F. EDDY, Carnegie Mellon University Chair, Committee on Applied and Theoretical Statistics Staff JOHN E. LAVERY, Director 10 NEVILLE, Administrative Secretary RUTH E. O'BRIEN, Staff Associate HANS OSER, Staff Officer JOHN R. TUCKER, Staff Officer JAMES A. voTrruK' Senior Staff Officer SCOTT T. WEIDMAN, Senior Staff Officer BARBARA WRIGHT, Administrative Assistant 1V

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COMMISSION ON PHYSICAL SCIENCES, MATHEMATICS, AND APPLICATIONS NORMAN HACKERMAN, Robert A. Welch Foundation, Chair PETER BICKEL, University of California at Berkeley GEORGE F. CARRIER, Harvard University (retired) DEAN E. EASTMAN, IBM TV. Watson Research Center MARYE ANNE Fox, University of Texas-Austin PHILLIP A. GRIFFITHS, Institute for Advanced Study NEAL F. LANE, Rice University RoBERT W. LUCKY, AT&T Bell Laboratories CLAIRE E. MAX, Lawrence Livermore Laboratory CHRISTOPHER F. MCKEE, University of California at Berkeley JAMES W. MITCHELL, AT&T Bell Laboratories RICHARD S. NIcHoLsoN' American Association for the Advancement of Science ALAN SCHRIESHEIM, Argonne National Laboratory KENNETH G. WILSON, Ohio State University NORMAN METZGER, Executive Director v

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