04763nam 2200541 i 45000010014000000030005000140050017000190060019000360070015000550080041000700100017001110200030001280200025001580280015001830350025001980350021002230400040002440500024002840820016003081000026003242450122003502640150004723000028006223360021006503370026006713380032006974900048007295040051007775051450008285060072022785201243023505300037035935380036036305380047036665880054037136500021037676500019037886530029038076530033038366530028038696530046038976530031039436550022039747100064039967760053040608300043041138560065041569781611974966SIAM20171004190106.0m o d cr |||||||||||170908s2017 pau ob 001 0 eng d a 2017031009 a9781611974966qelectronic z9781611974959qprint51aCS17bSIAM a(CaBNVSL)thg00974832 a(OCoLC)992437999 aCaBNVSLbengerdacCaBNVSLdCaBNVSL 4aQA433b.S525 2017eb04a515/.632231 aSidi, Avram,eauthor.10aVector extrapolation methods with applications /cAvram Sidi, Technion-Israel Institute of Technology, Haifa, Israel. 1aPhiladelphia, Pennsylvania :bSociety for Industrial and Applied Mathematics (SIAM, 3600 Market Street, Floor 6, Philadelphia, PA 19104),c[2017] a1 PDF (xiv, 433 pages). atext2rdacontent aelectronic2isbdmedia aonline resource2rdacarrier1 aComputational science and engineering ;v17 aIncludes bibliographical references and index.0 aPreface -- 0. Introduction and review of linear algebra -- part I. Vector extrapolation methods -- 1. Development of polynomial extrapolation methods -- 2. Unified algorithms for MPE and RRE -- 3. MPE and RRE are related -- 4. Algorithms for MMPE and SVD-MPE -- 5. Epsilon algorithms -- 6. Convergence study of extrapolation methods : part I -- 7. Convergence study of extrapolation methods : part II -- 8. Recursion relations for vector extrapolation methods -- part II. Krylov sybspace methods -- 9. Krylov subspace methods for linear systems -- 10. Krylov subspace methods for eigenvalue problems -- part III. Applications and generalizations -- 11. Miscellaneous applications of vector extrapolation methods -- 12. Rational approximations from vector-valued power series : part I -- 13. Rational approximations from vector-valued power series : part II -- 14. Applications of SMPE, SMMPE, and STEA -- 15. Vector generalizations of scalar extrapolation methods -- 16. Vector-valued rational interpolation methods -- part IV. Appendices -- Appendix A. QR factorization -- Appendix B. singular value decompositions (SVD) -- Appendix C. Moore-Penrose generalized inverse -- Appendix D. Basics of orthogonal polynomails -- Appendix E. Chebyshev polynomials : basic properties -- Appendix F. Useful formulas and results for Jacobi polynomials -- Appendix G. Rayleigh quotient and power method -- Appendix H. Unified FORTRAN77 code for MPE and RRE. aRestricted to subscribers or individual electronic text purchasers.3 aAn important problem that arises in different disciplines of science and engineering is that of computing limits of sequences of vectors of very large dimension. Such sequences arise, for example, in the numerical solution of systems of linear and nonlinear equations by fixed-point iterative methods, and their limits are simply the required solutions to these systems. The convergence of these sequences, which is very slow in many cases, can be accelerated successfully by using suitable vector extrapolation methods. Vector Extrapolation Methods with Applications is the first book fully dedicated to the subject of vector extrapolation methods. It is a self-contained, up-to-date, and state-of-the-art reference on the theory and practice of the most useful methods. It covers all aspects of the subject, including development of the methods, their convergence study, numerically stable algorithms for their implementation, and their various applications. It also provides complete proofs in most places. As an interesting application, the author shows how these methods give rise to rational approximation procedures for vector-valued functions in the complex plane, a subject of importance in model reduction problems among others. aAlso available in print version. aMode of access: World Wide Web. aSystem requirements: Adobe Acrobat Reader. aDescription based on title page of print version. 0aVector analysis. 0aExtrapolation. aConvergence acceleration aVector extrapolation methods aKrylov subspace methods aLarge sparse linear and nonlinear systems aVector iterative processes 0aElectronic books.2 aSociety for Industrial and Applied Mathematics,epublisher.08iPrint version:w(DLC) 2017026889z9781611974959 0aComputational science and engineering.403SIAMuhttp://epubs.siam.org/doi/book/10.1137/1.9781611974966