Numerical Analysis in Modern Scientific Computing [electronic resource] : An Introduction /

Numerical Analysis in Modern Scientific Computing [electronic resource] : An Introduction /

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This introductory book directs the reader to a selection of useful elementary numerical algorithms on a reasonably sound theoretical basis, built up within the text. The primary aim is to develop algorithmic thinking-emphasizing long-living computational concepts over fast changing software issues. The guiding principle is to explain modern numerical analysis concepts applicable in complex scientific computing at much simpler model problems. For example, the two adaptive techniques in numerical quadrature elaborated here carry the germs for either exploration methods or multigrid methods in differential equations, which are not treated here. The presentation draws on geometrical intuition wherever appropriate, supported by large number of illustrations. Numerous exercises are included for further practice and improved understanding. This text will appeal to undergraduate and graduate students as well as researchers in mathematics, computer science, science, and engineering. At the same time, it is addressed to practical computational scientists who, via self-study, wish to become acquainted with modern concepts of numerical analysis and scientific computing on an elementary level. The sole prerequisite is undergraduate knowledge in linear algebra and calculus.

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Auteurs principaux: Deuflhard, Peter. author., Hohmann, Andreas. author., SpringerLink (Online service)
Format: Texto biblioteca
Langue:eng
Publié: New York, NY : Springer New York, 2003
Sujets:Mathematics., Algebra., Computer mathematics., Numerical analysis., Probabilities., Physics., Computational intelligence., Numerical Analysis., Probability Theory and Stochastic Processes., Theoretical, Mathematical and Computational Physics., Computational Intelligence., Computational Mathematics and Numerical Analysis.,
Accès en ligne:http://dx.doi.org/10.1007/978-0-387-21584-6
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institution COLPOS
collection Koha
country México
countrycode MX
component Bibliográfico
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databasecode cat-colpos
tag biblioteca
region America del Norte
libraryname Departamento de documentación y biblioteca de COLPOS
language eng
topic Mathematics.
Algebra.
Computer mathematics.
Numerical analysis.
Probabilities.
Physics.
Computational intelligence.
Mathematics.
Numerical Analysis.
Probability Theory and Stochastic Processes.
Algebra.
Theoretical, Mathematical and Computational Physics.
Computational Intelligence.
Computational Mathematics and Numerical Analysis.
Mathematics.
Algebra.
Computer mathematics.
Numerical analysis.
Probabilities.
Physics.
Computational intelligence.
Mathematics.
Numerical Analysis.
Probability Theory and Stochastic Processes.
Algebra.
Theoretical, Mathematical and Computational Physics.
Computational Intelligence.
Computational Mathematics and Numerical Analysis.
spellingShingle Mathematics.
Algebra.
Computer mathematics.
Numerical analysis.
Probabilities.
Physics.
Computational intelligence.
Mathematics.
Numerical Analysis.
Probability Theory and Stochastic Processes.
Algebra.
Theoretical, Mathematical and Computational Physics.
Computational Intelligence.
Computational Mathematics and Numerical Analysis.
Mathematics.
Algebra.
Computer mathematics.
Numerical analysis.
Probabilities.
Physics.
Computational intelligence.
Mathematics.
Numerical Analysis.
Probability Theory and Stochastic Processes.
Algebra.
Theoretical, Mathematical and Computational Physics.
Computational Intelligence.
Computational Mathematics and Numerical Analysis.
Deuflhard, Peter. author.
Hohmann, Andreas. author.
SpringerLink (Online service)
Numerical Analysis in Modern Scientific Computing [electronic resource] : An Introduction /
description This introductory book directs the reader to a selection of useful elementary numerical algorithms on a reasonably sound theoretical basis, built up within the text. The primary aim is to develop algorithmic thinking-emphasizing long-living computational concepts over fast changing software issues. The guiding principle is to explain modern numerical analysis concepts applicable in complex scientific computing at much simpler model problems. For example, the two adaptive techniques in numerical quadrature elaborated here carry the germs for either exploration methods or multigrid methods in differential equations, which are not treated here. The presentation draws on geometrical intuition wherever appropriate, supported by large number of illustrations. Numerous exercises are included for further practice and improved understanding. This text will appeal to undergraduate and graduate students as well as researchers in mathematics, computer science, science, and engineering. At the same time, it is addressed to practical computational scientists who, via self-study, wish to become acquainted with modern concepts of numerical analysis and scientific computing on an elementary level. The sole prerequisite is undergraduate knowledge in linear algebra and calculus.
format Texto
topic_facet Mathematics.
Algebra.
Computer mathematics.
Numerical analysis.
Probabilities.
Physics.
Computational intelligence.
Mathematics.
Numerical Analysis.
Probability Theory and Stochastic Processes.
Algebra.
Theoretical, Mathematical and Computational Physics.
Computational Intelligence.
Computational Mathematics and Numerical Analysis.
author Deuflhard, Peter. author.
Hohmann, Andreas. author.
SpringerLink (Online service)
author_facet Deuflhard, Peter. author.
Hohmann, Andreas. author.
SpringerLink (Online service)
author_sort Deuflhard, Peter. author.
title Numerical Analysis in Modern Scientific Computing [electronic resource] : An Introduction /
title_short Numerical Analysis in Modern Scientific Computing [electronic resource] : An Introduction /
title_full Numerical Analysis in Modern Scientific Computing [electronic resource] : An Introduction /
title_fullStr Numerical Analysis in Modern Scientific Computing [electronic resource] : An Introduction /
title_full_unstemmed Numerical Analysis in Modern Scientific Computing [electronic resource] : An Introduction /
title_sort numerical analysis in modern scientific computing [electronic resource] : an introduction /
publisher New York, NY : Springer New York,
publishDate 2003
url http://dx.doi.org/10.1007/978-0-387-21584-6
work_keys_str_mv AT deuflhardpeterauthor numericalanalysisinmodernscientificcomputingelectronicresourceanintroduction
AT hohmannandreasauthor numericalanalysisinmodernscientificcomputingelectronicresourceanintroduction
AT springerlinkonlineservice numericalanalysisinmodernscientificcomputingelectronicresourceanintroduction
_version_ 1756268031343853568
spelling KOHA-OAI-TEST:2048502018-07-30T23:33:56ZNumerical Analysis in Modern Scientific Computing [electronic resource] : An Introduction / Deuflhard, Peter. author. Hohmann, Andreas. author. SpringerLink (Online service) textNew York, NY : Springer New York,2003.engThis introductory book directs the reader to a selection of useful elementary numerical algorithms on a reasonably sound theoretical basis, built up within the text. The primary aim is to develop algorithmic thinking-emphasizing long-living computational concepts over fast changing software issues. The guiding principle is to explain modern numerical analysis concepts applicable in complex scientific computing at much simpler model problems. For example, the two adaptive techniques in numerical quadrature elaborated here carry the germs for either exploration methods or multigrid methods in differential equations, which are not treated here. The presentation draws on geometrical intuition wherever appropriate, supported by large number of illustrations. Numerous exercises are included for further practice and improved understanding. This text will appeal to undergraduate and graduate students as well as researchers in mathematics, computer science, science, and engineering. At the same time, it is addressed to practical computational scientists who, via self-study, wish to become acquainted with modern concepts of numerical analysis and scientific computing on an elementary level. The sole prerequisite is undergraduate knowledge in linear algebra and calculus.1 Linear Systems -- 1.1 Solution of Triangular Systems -- 1.2 Gaussian Elimination -- 1.3 Pivoting Strategies and Iterative Refinement -- 1.4 Cholesky Decomposition for Symmetric Positive Definite Matrices -- Exercises -- 2 Error Analysis -- 2.1 Sources of Errors -- 2.2 Condition of Problems -- 2.3 Stability of Algorithms -- 2.4 Application to Linear Systems -- Exercises -- 3 Linear Least-Squares Problems -- 3.1 Least-Squares Method of Gauss -- 3.2 Orthogonalization Methods -- 3.3 Generalized Inverses -- Exercises -- 4 Nonlinear Systems and Least-Squares Problems -- 4.1 Fixed-Point Iterations -- 4.2 Newton Methods for Nonlinear Systems -- 4.3 Gauss-Newton Method for Nonlinear Least-Squares Problems -- 4.4 Nonlinear Systems Depending on Parameters -- Exercises -- 5 Linear Eigenvalue Problems -- 5.1 Condition of General Eigenvalue Problems -- 5.2 Power Method -- 5.3 QR-Algorithm for Symmetric Eigenvalue Problems -- 5.4 Singular Value Decomposition -- 5.5 Stochastic Eigenvalue Problems -- Exercises -- 6 Three-Term Recurrence Relations -- 6.1 Theoretical Background -- 6.2 Numerical Aspects -- 6.3 Adjoint Summation -- Exercises -- 7 Interpolation and Approximation -- 7.1 Classical Polynomial Interpolation -- 7.2 Trigonometric Interpolation -- 7.3 Bézier Techniques -- 7.4 Splines -- Exercises -- 8 Large Symmetric Systems of Equations and Eigenvalue Problems -- 8.1 Classical Iteration Methods -- 8.2 Chebyshev Acceleration -- 8.3 Method of Conjugate Gradients -- 8.4 Preconditioning -- 8.5 Lanczos Methods -- Exercises -- 9 Definite Integrals -- 9.1 Quadrature Formulas -- 9.2 Newton-Cotes Formulas -- 9.3 Gauss-Christoffel Quadrature -- 9.4 Classical Romberg Quadrature -- 9.5 Adaptive Romberg Quadrature -- 9.6 Hard Integration Problems -- 9.7 Adaptive Multigrid Quadrature -- Exercises -- References -- Software.This introductory book directs the reader to a selection of useful elementary numerical algorithms on a reasonably sound theoretical basis, built up within the text. The primary aim is to develop algorithmic thinking-emphasizing long-living computational concepts over fast changing software issues. The guiding principle is to explain modern numerical analysis concepts applicable in complex scientific computing at much simpler model problems. For example, the two adaptive techniques in numerical quadrature elaborated here carry the germs for either exploration methods or multigrid methods in differential equations, which are not treated here. The presentation draws on geometrical intuition wherever appropriate, supported by large number of illustrations. Numerous exercises are included for further practice and improved understanding. This text will appeal to undergraduate and graduate students as well as researchers in mathematics, computer science, science, and engineering. At the same time, it is addressed to practical computational scientists who, via self-study, wish to become acquainted with modern concepts of numerical analysis and scientific computing on an elementary level. The sole prerequisite is undergraduate knowledge in linear algebra and calculus.Mathematics.Algebra.Computer mathematics.Numerical analysis.Probabilities.Physics.Computational intelligence.Mathematics.Numerical Analysis.Probability Theory and Stochastic Processes.Algebra.Theoretical, Mathematical and Computational Physics.Computational Intelligence.Computational Mathematics and Numerical Analysis.Springer eBookshttp://dx.doi.org/10.1007/978-0-387-21584-6URN:ISBN:9780387215846

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