国外数学名著系列（影印版）5：数值数学简介，目录书摘

2020-03-13 09:45 来源：京东作者：京东

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内容简介:　　数值数学是数学的一个分支，它提出、发展、分析并应用科学计算中的方法于若干领域，如分析学、线性代数、几何学、逼近论、函数方程、优化问题和微分方程等等。而其他领域，如物理学、自然和生物科学、工程、经济、金融科学也经常提出问题，而问题的解决同样需要科学计算。
　　因此可以说，数值数学是现代应用科学中具有很强相关性的不同学科的一个交叉学科，是这些学科中定性和定量分析的重要工具。
　　写作《国外数学名著系列5：数值数学（影印版）》的目的之一，是给出数值方法的数学基础，分析其基本的理论性质（如稳定性、精度、计算复杂性），应用MATLAB这一界面友好并被广泛接受的软件，通过例子和反例说明其特征和优缺点。讨论每一类问题时，都评述*适合的算法，进行理论分析，并利用_AMATLAB程序验证理论结果。书中每一章都包含例子、练习，并运用所讨论的理论解决现实生活中的问题。
　　《国外数学名著系列5：数值数学（影印版）》主要写给本科高年级学生及工程、数学、物理和计算机科学各专业研究生，而强调应用性和对相关软件的发展的关注，也使《国外数学名著系列5：数值数学（影印版）》对各种专业领域的研究人员和科学计算的实践者都颇有价值。

作者简介:

目录:Preface
I．Getting Started
1．Foundations of Matrix Analysis
1．1 Vector Spaces
1．2 Matrices
1．3 Operations with Matrices
1．3．1 Inverse of a Matrix
1．3．2 Matrices and Linear Mappings
1．3．3 Operations with Block-Partitioned Matrices
1．4 Trace and Determinant of a Matrix
1．5 Rank and Kernel of a Matrix
1．6 Special Matrices
1．6．1 Block Diagonal Matrices
1．6．2 Trapezoidaland Triangular Matrices
1．6．3 Banded Matrices
1．7 Eigenvalues and Eigenvectors
1．8 Similarity Transformations
1．9 The Singular Value Decomposition （SVD）
1．10 Scalar Product and Norms in Vector Spaces
1．11 Matrix Norms
1．11．1 Relation between Norms and the Spectral Radius of a Matrix
1．11．2 Sequences and Series of Matrices
1．12 Positive Definite，Diagonally Dominant and M-matrices
1．13 Exercises
2．Principles of Numerical Mathematics
2．1 Well-posedness and Condition Number of a Problem
2．2 Stability of Numerical Methods
2．2．1 Relations between Stability and Convergence
2．3 A priori and a posteriori Analysis
2．4 Sources of Error in Computational Models
2．5 Machine Representation of Numbers
2．5．1 The Positional System
2．5．2 The Floating-point Number System
2．5．3 Distribution of Floating-point Numbers
2．5．4 IEClIEEE Arithmetic
2．5．5 Rounding of a Real Number in its Machine Repre sentation
2．5．6 Machine Floating-point Operations
2．6 Exercises

II．Numerical Linear Algebra
3．Direct Methods for the Solution of Linear Systems
3．1 Stability Analysis of Linear Systems
3．1．1 The Condition Number of a Matrix
3．1．2 Forward a priori Analysis
3．1．3 Backward a priori Analysis
3．1．4 A posteriori Analysis
3．2 Solution of Triangular Systems
3．2．1 Implementation of Substitution Methods
3．2．2 Rounding Error Analysis
3．2．3 Inverse of a Triangular Matrix
3．3 The Gaussian Elimination Method （GEM） and LU Factorization
3．3．1 GEM as a Factorization Method
3．3．2 The Effect of Rounding Errors
3．3．3 Implementation of LU Factorization
3．3．4 Compact Forms of Factorization
3．4 Other Types of Factorization
3．4．1 LDMT Factorization
……
III．Around Functions and Functionals
IV．Transforms，Differentiation and Problem Dis-cretication
References
Index of MATLAB Programs
Index

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