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Titlebook: Numerical Mathematics; Alfio Quarteroni,Riccardo Sacco,Fausto Saleri Textbook 20071st edition Springer Science+Business Media New York 200

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发表于 2025-3-21 18:57:02 | 显示全部楼层 |阅读模式
书目名称Numerical Mathematics
编辑Alfio Quarteroni,Riccardo Sacco,Fausto Saleri
视频video
丛书名称Texts in Applied Mathematics
图书封面Titlebook: Numerical Mathematics;  Alfio Quarteroni,Riccardo Sacco,Fausto Saleri Textbook 20071st edition Springer Science+Business Media New York 200
描述Numerical mathematics is the branch of mathematics that proposes, develops, analyzes and applies methods from scientific computing to several fields including analysis, linear algebra, geometry, approximation theory, functional equations, optimization and differential equations. Other disciplines, such as physics, the natural and biological sciences, engineering, and economics and the financial sciences frequently give rise to problems that need scientific computing for their solutions..As such, numerical mathematics is the crossroad of several disciplines of great relevance in modern applied sciences, and can become a crucial tool for their qualitative and quantitative analysis..One of the purposes of this book is to provide the mathematical foundations of numerical methods, to analyze their basic theoretical properties (stability, accuracy, computational complexity) and demonstrate their performances on examples and counterexamples which outline their pros and cons. This is done using the MATLAB software environment which is user-friendly and widely adopted. Within any specific class of problems, the most appropriate scientific computing algorithms are reviewed, their theoretical
出版日期Textbook 20071st edition
关键词Algebra; MATLAB; algorithms; calculus; complexity; equation; function; geometry; linear algebra; mathematics;
版次1
doihttps://doi.org/10.1007/978-0-387-22750-4
isbn_ebook978-0-387-22750-4Series ISSN 0939-2475 Series E-ISSN 2196-9949
issn_series 0939-2475
copyrightSpringer Science+Business Media New York 2007
The information of publication is updating

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0939-2475 l fields including analysis, linear algebra, geometry, approximation theory, functional equations, optimization and differential equations. Other disciplines, such as physics, the natural and biological sciences, engineering, and economics and the financial sciences frequently give rise to problems
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Textbook 20071st editionncluding analysis, linear algebra, geometry, approximation theory, functional equations, optimization and differential equations. Other disciplines, such as physics, the natural and biological sciences, engineering, and economics and the financial sciences frequently give rise to problems that need
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Approximation of Eigenvalues and EigenvectorsIn this chapter we deal with approximations of the eigenvalues and eigen-vectors of a matrix A ∈ ℂ. Two main classes of numerical methods exist to this purpose, . methods, which compute the . eigen-values of A (that is, those having maximum and minimum module), or . methods, which approximate the whole spectrum of A.
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Orthogonal Polynomials in Approximation TheoryTrigonometric polynomials, as well as other orthogonal polynomials like Legendre’s and Chebyshev’s, are widely employed in approximation theory.
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Two-Point Boundary Value ProblemsThis chapter is devoted to the analysis of approximation methods for two-point boundary value problems for differential equations of elliptic type. Finite differences, finite elements and spectral methods will be considered. A short account is also given on the extension to elliptic boundary value problems in two-dimensional regions.
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