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Numerik-Algorithmen mit FORTRAN 77-Programmen. Selections. English
1 online resource (xxii, 596 pages) : illustrations
The book gives an informal introduction to mathematical and computational principles governing numerical analysis, as well as practical guidelines for using over 130 elaborate numerical analysis routines. It develops detailed formulas for both standard and rarely found algorithms, including many variants for linear and non-linear equation solvers, one- and two-dimensional splines of various kinds, numerical quadrature and cubature formulas of all known stable orders, and stable IVP and BVP solvers, even for stiff systems of differential equations. The descriptions of the algorithms are very detailed and focus on their implementation, giving sensible decision criteria to choose among the algorithms and describing the merits and demerits of each one. The authors see "Numerical Algorithms with C" as a depository of highly useful and effective algorithms and codes for the scientist and engineer who needs to have direct access to such algorithms. The programs are all field tested. The enclosed CD-ROM contains all computer codes, a compiler and a test bed of programs and data for most of the algorithms. Each test program includes detailed comments and describes available options, all clearly marked, with a complete list of error codes, etc.
Computer numbers, error analysis, conditioning, stability of algorithms and operations count -- Nonlinear equations in one variable -- Roots of polynomials -- Direct methods for solving systems of linear equations -- Iterative methods for linear systems -- Systems of nonlinear equations -- Eigenvalues and eigenvectors of matrices -- Linear and nonlinear approximation -- Polynomial and rational interpolation -- Interpolating polynomial splines for constructing smooth curves -- Cubic fitting splines for constructing smooth curves -- Two-dimensional splines, surface splines, bezier splines, b-splines -- Akima and renner subsplines -- Numerical differentiation -- Numerical integration -- Numerical cubature -- Initial value problems for ordinary differential equations -- Boundary value problems for ordinary differential equations.
Gisela Engeln-Müllges, Frank Uhlig ; translated by Maria Schon and Frank Uhlig.
Electronic version lacks CD-ROM content that accompanied print book
Includes bibliographical references (pages 569-590) and index.