{"product_id":"krylov-solvers-for-linear-algebraic-systems-krylov-solvers","title":"Krylov Solvers for Linear Algebraic Systems: Krylov Solvers","description":"The first four chapters of this book give a comprehensive and unified theory of the Krylov methods. Many of these are shown to be particular examples of\u003cbr\u003ethe block conjugate-gradient algorithm and it is this observation that\u003cbr\u003epermits the unification of the theory. The two major sub-classes of those\u003cbr\u003emethods, the Lanczos and the Hestenes-Stiefel, are developed in parallel as\u003cbr\u003enatural generalisations of the Orthodir (GCR) and Orthomin algorithms. These\u003cbr\u003eare themselves based on Arnoldi's algorithm and a generalised Gram-Schmidt\u003cbr\u003ealgorithm and their properties, in particular their stability properties,\u003cbr\u003eare determined by the two matrices that define the block conjugate-gradient\u003cbr\u003ealgorithm. These are the matrix of coefficients and the preconditioning\u003cbr\u003ematrix.\u003cbr\u003e\u003cbr\u003eIn Chapter 5 the\"transpose-free\" algorithms based on the conjugate-gradient squared algorithm are presented while Chapter 6 examines the various ways in which the QMR technique has been exploited. Look-ahead methods and general block methods are dealt with in Chapters 7 and 8 while Chapter 9 is devoted to error analysis of two basic algorithms.\u003cbr\u003e\u003cbr\u003eIn Chapter 10 the results of numerical testing of the more important algorithms in their basic forms (i.e. without look-ahead or preconditioning) are presented and these are related to the structure of the algorithms and the general theory. Graphs illustrating the performances of various algorithm\/problem combinations are given via a CD-ROM.\u003cbr\u003e\u003cbr\u003eChapter 11, by far the longest, gives a survey of preconditioning techniques. These range from the old idea of polynomial preconditioning via SOR and ILU preconditioning to methods like SpAI, AInv and the multigrid methods that were developed specifically for use with parallel computers. Chapter 12 is devoted to dual algorithms like Orthores and the reverse algorithms of Hegedus. Finally certain ancillary matters like reduction to Hessenberg form, Chebychev polynomials and the companion matrix are described in a series of appendices.\u003cbr\u003e\u003cbr\u003e·\tcomprehensive and unified approach\u003cbr\u003e·\tup-to-date chapter on preconditioners\u003cbr\u003e·\tcomplete theory of stability\u003cbr\u003e·\tincludes dual and reverse methods\u003cbr\u003e·\tcomparison of algorithms on CD-ROM\u003cbr\u003e·\tobjective assessment of algorithms","brand":"Elsevier S \u0026 T","offers":[{"title":"perpetual","offer_id":45044003504225,"sku":"9780444514745","price":87.0,"currency_code":"KWD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0268\/9869\/4241\/files\/480_397407c9-349e-42ae-9725-5ffc83108a31.jpg?v=1779750053","url":"https:\/\/ebooks.aafaqeducation.com\/products\/krylov-solvers-for-linear-algebraic-systems-krylov-solvers","provider":"ebook.aafaqeducation","version":"1.0","type":"link"}