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001 sulb-eb0022927
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008 131206s2013 xxu| s |||| 0|eng d
020 _a9781461484530
_9978-1-4614-8453-0
024 7 _a10.1007/978-1-4614-8453-0
_2doi
050 4 _aQA71-90
072 7 _aPBKS
_2bicssc
072 7 _aMAT006000
_2bisacsh
082 0 4 _a518
_223
100 1 _aCorless, Robert M.
_eauthor.
245 1 2 _aA Graduate Introduction to Numerical Methods
_h[electronic resource] :
_bFrom the Viewpoint of Backward Error Analysis /
_cby Robert M. Corless, Nicolas Fillion.
264 1 _aNew York, NY :
_bSpringer New York :
_bImprint: Springer,
_c2013.
300 _aXXXIX, 869 p. 194 illus., 10 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
505 0 _aComputer Arithmetic & Fundamental Concepts of Computation -- Polynomials and Series -- Rootfinding and Function Evaluation -- Solving Ax = b .- Solving Ax =l x -- Structured Linear Systems.-Iterative Methods -- Polynomial and Rational Interpolation -- The Discrete Fourier Transform -- Numerical Integration -- Numerical Differentiation and Finite Differences -- Numerical Solution of ODEs --  Numerical Methods for ODEs.- Numerical Solutions of Boundary Value Problems -- Numerical Solution of Delay DEs -- Numerical Solution of PDEs.
520 _aThis book provides an extensive introduction to numerical computing from the viewpoint of backward error analysis. The intended audience includes students and researchers in science, engineering and mathematics. The approach taken is somewhat informal owing to the wide variety of backgrounds of the readers, but the central ideas of backward error and sensitivity (conditioning) are systematically emphasized. The book is divided into four parts: Part I provides the background preliminaries including floating-point arithmetic, polynomials and computer evaluation of functions; Part II covers numerical linear algebra; Part III covers interpolation, the FFT and quadrature; and Part IV covers numerical solutions of differential equations including initial-value problems, boundary-value problems, delay differential equations and a brief chapter on partial differential equations. The book contains detailed illustrations, chapter summaries and a variety of exercises as well as some Matlab codes provided online as supplementary material.   “I really like the focus on backward error analysis and condition. This is novel in a textbook and a practical approach that will bring welcome attention." Lawrence F. Shampine.
650 0 _aMathematics.
650 0 _aComputer mathematics.
650 0 _aNumerical analysis.
650 1 4 _aMathematics.
650 2 4 _aComputational Mathematics and Numerical Analysis.
650 2 4 _aComputational Science and Engineering.
650 2 4 _aNumerical Analysis.
700 1 _aFillion, Nicolas.
_eauthor.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9781461484523
856 4 0 _uhttp://dx.doi.org/10.1007/978-1-4614-8453-0
912 _aZDB-2-SMA
942 _2Dewey Decimal Classification
_ceBooks
999 _c45019
_d45019