41. Householder Transformation Method We now develop the method attributed to alston Scott householder (May 5, 1904 July4, 1993) which is routinely taught in courses in linear algebra, http://math.fullerton.edu/mathews/n2003/HouseholderMod.html

Module for Householder Transformations Householder's Method Each transformation in Jacobi's method produced two zero off-diagonal elements, but subsequent iterations might make them nonzero. Hence many iterations are required to make the off-diagonal entries sufficiently close to zero. Suppose that A is a real symmetric matrix. Householder's method is used to construct a similar symmetric tridiagonal matrix. Then the QR method can be used to find all eigenvalues of the tridiagonal matrix. We now develop the method attributed to Alston Scott Householder (May 5, 1904 - July4, 1993) which is routinely taught in courses in linear algebra, and numerical analysis. Several several zero off-diagonal elements are created with each iteration, and they remain zero in subsequent iterations. We start by developing an important step in the process. Theorem (Householder Reflection) If and are vectors with the same norm, there exists an orthogonal symmetric matrix such that where and Since is both orthogonal and symmetric, it follows that

42. Graeffe's Method alston S. householder The American Mathematical Monthly, Vol. 66, No. 6. (Jun . alston S. householder McGrawHill Book Co., Inc., (1953), New York, pp. http://math.fullerton.edu/mathews/n2003/graeffemethod/GraeffeMethodBib/Links/Gra

Bibliography for Graeffe's Method unabridged On zeros of polynomial and vector solutions of associated polynomial system from Vieta theorem. Wu, Xinyuan Appl. Numer. Math. 44 (2003), no. 3, 415423, MathSciNet. Jacobi-Free and Complex-Free Method for Finding Simultaneously All Zeros of Polynomials Having only Real Zeros Wu, Xingyuan; Shao, Rong; Yiran, Z.H.U. Computers and Mathematics with Applications, v 46, n 8-9, October/November, 2003, p 1387-1395, Compendex. Tangent Graeffe iteration. Malajovich, Gregorio; Zubelli, Jorge P. Numer. Math. 89 (2001), no. 4, 749782, MathSciNet. Iterative methods for roots of polynomials Mekwi, W.R. Masters thesis, (2001), University of Oxford, U. K. On the Geometry of Graeffe Iteration Malajovich, G.; Zubelli, J. P. Journal of Complexity, 2001, vol. 17, no. 3, pp. 541-573, Ingenta. A generalized Graeffe's iteration for evaluating polynomials and rational functions Gemignani, Luca Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC, 2001, p 143-149, Compendex.

43. The MathWorks - MATLAB News & Notes - December 2004 - Cleve's Corner - The Origi alston householder from Oak Ridge National Laboratory and the University ofTennessee began a series of research conferences on numerical algebra in the http://www.mathworks.com/company/newsletters/news_notes/clevescorner/dec04.html

var host_pre = "http://www"; Home Select Country Contact Us Store Search Create Account Log In Industries Academia ... Past Issues MATLAB Digest July 2005 May 2005 Past Issues February 2005 ... Past Issues Automotive Digest April 2005 October 2004 Past Issues Contact sales ... Print this page Video: The Origins of MATLAB Cleve Moler describes his inspiration for authoring MATLAB. (8:17) View in QuickTime View in Windows Media Cleve's Corner The Origins of MATLAB by Cleve Moler With 2004 marking the 20th anniversary of The MathWorks, it’s a good time to look back at the origins of MATLAB. Wilkinson was a British mathematician who spent his entire career at the National Physical Laboratory (NPL) in Teddington, outside London. Working on a simplified version of a sophisticated design by Alan Turing, Wilkinson and colleagues at NPL built the Pilot Automatic Computing Engine (ACE), one of Britain’s first stored-program digital computers. The Pilot ACE ran its first program in May 1950. Wilkinson did matrix computations on the machine and went on to become the world’s leading authority on numerical linear algebra. At about the same time, mathematicians at the Institute for Numerical Analysis (INA), a branch of the National Bureau of Standards, located at UCLA, were working with the Standards Western Automatic Computer (SWAC), one of the USA’s first computers. Researchers at INA included George Forsythe, John Todd, and Olga Taussky-Todd. When the INA dissolved in 1957, Forsythe joined the faculty at Stanford and the Todds joined the faculty at Caltech.

44. Information Processing Bibliographies (New York, NY American Institute of Electrical Engineers, 1954) (Box 1, Folder46); householder, alston S. Bibliography on numerical analysis. http://www.cbi.umn.edu/collections/inv/cbi00091.html

Information Processing Bibliographies, 1947-[ongoing] CBI 91 1.25 cubic feet in 2 boxes By: Kevin D. Corbitt, August 1994 ACQUISITION: The records were given to the Charles Babbage Institute by various institutions, corporations, and individuals in numerous accessions. ACCESS: The collection is unrestricted. Please cite the collection as follows: Information Processing Bibliographies (CBI 91), Charles Babbage Institute, University of Minnesota, Minneapolis. Scope and Content Bibliographies collected by the Charles Babbage Institute on various ascpects of information processing. INVENTORY Bibliography of machines for solving algebraic equations. : Self published, 1947) (Box 1, Folder 55) Computing devices bibliography. : Self published, 1950) (Box 1, Folder 54) Aitken, Hugh G. J.; Robert B. Stoddard. History of computers and computer languages: A preliminary bibliography. (Amherst, MA: Self published, 1982) (Box 1, Folder 37) American Institute of Electrical Engineers. Committee on Computing Devices. Bibliography Subcommittee. Bibliography on computing devices. (Philadelphia, PA: American Institute of Electrical Engineers, 1953) (Box 2, Folder 3) Armed Services Technical Information Agency. Documentation. (Arlington, VA: Armed Services Technical Information Agency, 1962) (Box 1, Folder 16)

45. Unitary Triangularization Of A Nonsymmetric Matrix alston S. householder, Oak Ridge National Laboratory, Oak Ridge, Tennessee 1 AS householder (1958), A class of methods for inverting matrices. J. Soc. http://portal.acm.org/citation.cfm?id=320947

46. Calculation Of Generalized Hypergeometric Series 2 householder, alston S., 19S3 Principles of Numerical Analysis. alston S.householder, Bibliography on Numerical Analysis, Journal of the ACM (JACM), http://portal.acm.org/citation.cfm?id=320783.320785

47. The Top Ten Algorithms Of The Century developed by Magnus Hestenes, Eduard Stiefel, and Cornelius Lanczos;;the householder matrix decomposition, developed by alston householder; http://www.csit.fsu.edu/~burkardt/fun/misc/algorithms_dongarra.html

The Top Ten Algorithms of the Century Dongarra and Sullivan Jack Dongarra and Francis Sullivan published a list of "The Top Ten Algorithms of the Century." Their list included: the Monte Carlo method or Metropolis algorithm, devised by John von Neumann, Stanislaw Ulam, and Nicholas Metropolis; the simplex method of linear programming, developed by George Dantzig; the Krylov Subspace Iteration method, developed by Magnus Hestenes, Eduard Stiefel, and Cornelius Lanczos; the Householder matrix decomposition, developed by Alston Householder; the Fortran compiler, developed by a team lead by John Backus; the QR algorithm for eigenvalue calculation, developed by J Francis; the Quicksort algorithm, developed by Anthony Hoare; the Fast Fourier Transform, developed by James Cooley and John Tukey; the Integer Relation Detection Algorithm, developed by Helaman Ferguson and Rodney Forcade; (given N real values X I , is there a nontrivial set of integer coefficients A I so that sum ( 1 <= I <= N ) A I * X I the fast Multipole algorithm, developed by Leslie Greengard and Vladimir Rokhlin; (to calculate gravitational forces in an N-body problem normally requires N^2 calculations. The fast multipole method uses order N calculations, by approximating the effects of groups of distant particles using multipole expansions)

48. New Page 1 and Least Squares) has new material on block householder computations. pleasure that we dedicate the new volume to both him and alston householder. http://www.cs.cornell.edu/cv/Books/GVL/GVL2Pref.htm

Matrix Computations Preface to the Second Edition (1989) We were motivated to write a revised and expanded version of Matrix Computation for two reasons. First, after five years of teaching from the old edition and hearing from colleagues, it became clear that much of what we wrote could be written better. Many of the proofs and derivations have been clarified and we have adopted a stylized Matlab notation that facilitates matrix/vector thinking. Another new stylistic feature of the new edition is the classification of material down to the subsection level. This should make the volume easier to use as a textbook and as a reference. The second reason for the new edition has to do with the blossoming of the parallel matrix computation area. The multiprocessor is revolutionizing the role of computation in science and engineering and it is crucial that we document the contributions of numerical linear algebra to this process. We do so in a machine-independent way that stresses high-level algorithmic ideas in preference to specific implementations. As we say in the new chapter on parallel matrix computations, the field is very fluid and the literature is overwhelmed with case studies. Nevertheless, there are a handful of key algorithmic developments that are likely to be with us for a long time and these are most definitely ready for textbook level discussion. Here is a chapter-by-chapter tour of what is new in the Second Edition: In Chapter 1 (Matrix Multiplication Problems) we introduce notation and fundamental concepts using matrix multiplication as an example. Block matrix manipulation is given a very high profile and we have added a new section on vector pipeline computing.

49. Scientific & Parallel Computing Folklore quip, circa 1960 attributed to alston householder. Scientists andengineers rely more than ever on computer modeling and simulation to buttress http://www.cs.cornell.edu/Research/scientif/

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50. Enciclopedia :: 100cia.com Translate this page alston householder. (En este momento no hay texto en esta p�gina. Para iniciarel art�culo, click editar esta p�gina (http//es.wikipedia. http://100cia.com/enciclopedia/Alston_Householder

Portada Artículos favoritos Vea sus documentos y artículos favoritos pulsando aquí No hay artículos favoritos todavía. documentos sin leer: Siguiente doc sin leer Borrar los docs leídos Borrar todos los docs ¡Webmaster! ¿Quieres tener los contenidos de 100cia.com en tu página? Pulsa aquí Buscar: en Google en noticias en Enciclopedia Estás en: 100cia.com > Enciclopedia Alston Householder (En este momento no hay texto en esta p�gina. Para iniciar el art�culo, click editar esta p�gina http://es.wikipedia.orgAlston_Householder Información de Wikipedia (Licencia de uso GFDL) e Internet ¿Sabías que Albert Einstein dijo...? No podemos resolver problemas usando el mismo tipo de pensamiento que usamos cuando los cremos. Acerca de Sync.es Webs amigas: AstroRED CanalGame AweZoom

51. From Paul Vandooren Vandooren@csam.ucl.ac.be Subject LAST REMINDER householder AWARD X Nominations are solicited for the alston S . to recognize the outstanding contributions of alston S. householder, http://www.scicomp.uni-erlangen.de/letter/v99n02/g0

From: Paul Vandooren

52. From Nick Higham Higham@maths.man.ac.uk Subject Householder +0100 (BST) householder AWARD XI Nominations are solicited for the alston S . to recognize the outstanding contributions of alston S. householder, http://www.scicomp.uni-erlangen.de/letter/v01n07/g2

From: Nick Higham

53. The Computer Journal -- Sign In Page http://comjnl.oxfordjournals.org/cgi/reprint/12/4/392

JOURNAL HOME HELP FEEDBACK SUBSCRIPTIONS ... SEARCH QUICK SEARCH: [advanced] Author: Keyword(s): Year: Vol: Page: This item requires a subscription* to The Computer Journal Online. * Please note that articles prior to 1996 are not normally available via a current subscription. In order to view content before this time, access to the Oxford Journals digital archive is required. Alternatively, you may purchase short-term access on a Pay per Article basis. Please see below for more details. PDF Alston S. Householder Award The Computer Journal. This Article Alert me when this article is cited Alert me if a correction is posted Services Email this article to a friend Similar articles in this journal Alert me to new issues of the journal Download to citation manager ... Request Permissions To view this item, select one of the options below: Sign In User Name Sign in without cookies. Can't get past this page? Help with Cookies. Need to Activate? Password Forgot your user name or password? Purchase Short-Term Access Pay per Article - You may access this article (from the computer you are currently using) for 1 day for US$23.00

54. NCSU/CSC: Robert E. Funderlic under the direction of Professor alston householder. Dr. Funderlic s main interestslie in the design, implementation and analysis of numerical linear http://www.csc.ncsu.edu/faculty/ref/

Robert E. Funderlic Professor Ph. D., University of Tennessee, 1970 under the direction of Professor Alston Householder. Dr. Funderlic's main interests lie in the design, implementation and analysis of numerical linear algebra algorithms for high performance computing. His students often have close ties with the North Carolina Supercomputing Center with its IBM-SP and other advanced architectures. His interests span over most areas of numerical analysis and intersect with several diverse applications including most recently matrix factorizations applicable to data mining (current NSF Grant Abstract ), and atmospheric and environmental models ( related current (student) Andy Smith Ph.D. research ). [Dr. F. was department head from 1986 to 1992] Representative Publications "Optimizing Performance of Parallel Architectures Through Processor configuration and Data Distribution," (with C.D Wong, E.W. Davis and F. A. Smith) Journal of Parallel and Distributed Computing (under review). "The Centroid Decomposition: Relationships Between Discrete Variational Decompositions and SVD," (with M. Chu)

55. 78. DOE/ORNL - Alston S. Householder Fellowship In Scientific Computing DOE/ORNL alston S. householder Fellowship in Scientific Computing. The ComputerScience and Mathematics (CSM) Division at the Oak Ridge National http://apps.rgp.ufl.edu/research/fyi/back_issues/v27n15/fyi078.cfm

Division of Sponsored Research Sponsored Research Graduate School Technology Licensing UF Research Foundation ... Next Publication Date - 2/4/2000 78. DOE/ORNL - Alston S. Householder Fellowship in Scientific Computing The Computer Science and Mathematics (CSM) Division at the Oak Ridge National Laboratory (ORNL) invites outstanding candidates to apply for the 2000 Alston S. Householder Fellowship in Scientific Computing. The purpose of the Householder Fellowship is to promote innovative research in scientific computing on advanced computer architectures and to facilitate technology transfer from the laboratory research environment to industry and academia through advanced training of new computational scientists. Each Householder Fellowship carries a one-year appointment, potentially renewable, in the ORNL CSM Division, with competitive salary, fringe benefits and travel opportunities. The Fellowship requires a Ph.D. in computer science, mathematics or statistics, completed no more than three years prior to the appointment. Applicants must have a strong background and research interest in large-scale scientific computing. Applicants should send a resume, statement of research and three letters of recommendation by

56. Alston, Walter --  Britannica Student Encyclopedia alston Scott householder University of St.Andrews, Scotland Brief note on thelife and works of this American mathematician known for his research in http://www.britannica.com/ebi/article-9309797

Home Browse Newsletters Store ... Subscribe Already a member? Log in This Article's Table of Contents Walter Alston Print this Table of Contents Shopping Price: USD $1495 Revised, updated, and still unrivaled. The Official Scrabble Players Dictionary (Hardcover) Price: USD $15.95 The Scrabble player's bible on sale! Save 30%. Merriam-Webster's Collegiate Dictionary Price: USD $19.95 Save big on America's best-selling dictionary. Discounted 38%! More Britannica products Alston, Walter  Student Encyclopedia Article Page 1 of 1 Walter Alston Walter Alston. Bettmann/Corbis Alston, Walter... (75 of 649 words) var mm = [["Jan.","January"],["Feb.","February"],["Mar.","March"],["Apr.","April"],["May","May"],["June","June"],["July","July"],["Aug.","August"],["Sept.","September"],["Oct.","October"],["Nov.","November"],["Dec.","December"]]; To cite this page: MLA style: "Alston, Walter." Britannica Student Encyclopedia http://www.britannica.com/ebi/article-9309797

57. LOUIS COLLINS BOOKS ABAA: Principles Of Numerical Analysis. By HOUSEHOLDER (Alst NY McGraw Hill, 1953.. later printing, 274pp. octavo. bookstore stamp,......Title Principles of Numerical Analysis. Author householder (alston). http://www.collinsbooks.com/cgi-bin/lcb455/13922.html

Browse by category Africa Americana Anthropology Archaeology Architecture Automotive Books about books Cinema Closet of Serendip Cookery Criminology Geography Geology History History - Europe Juvenile Linguistics Literature Medicine Music Natural History Philosophy Politics Psychology Religion Science Serendip Technology Transportation Quick Search Log In Username: Password: Create an account About Us LOUIS COLLINS BOOKS ABAA more Contact Us Terms Security ... Site Map LOUIS COLLINS BOOKS ABAA 1211 East Denny Way Seattle, WA 98122 This site is powered by Bibliopolis Title: Principles of Numerical Analysis. Author: HOUSEHOLDER (Alston). Description: NY:: McGraw Hill, 1953.. later printing, 274pp. octavo. bookstore stamp, ink note, cover wear otherwise very good. Item # Add to your cart We accept VISA/ MasterCard/American Express. Books are returnable within 10 business days. DOMESTIC POSTAGE : Postage is extra. Please add per order for MEDIA MAIL (6-8 days delivery); per order for PRIORITY MAIL (2-3 days) FOREIGN POSTAGE : Postage is extra on ALL orders.

58. UW Libraries - Database Search Author, householder, alston Scott, 1904. Subject, Electronic digital computersNumerical analysis. Keywords, 1904 (23), alston (2), analysis (728), http://www.lib.washington.edu/resource/search/ResFull.asp?Field=record&ID=17615

59. UW Libraries - Database Search digital (885), electronic (776), householder, mathematik (20), numerical (64),numerische, 1953 (76), agriculture (1010), alston (2), aspects (907), http://www.lib.washington.edu/resource/search/ResFull.asp?Field=keyword&ID=84152

60. Alston Householder Université Montpellier II Translate this page alston householder (1904-1993). Cette image et la biographie complète en anglaisrésident sur le site de l’université de St Andrews Écosse http://ens.math.univ-montp2.fr/SPIP/article.php3?id_article=1307

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