| 要使我国的数学事业更好地发展起来，需要数学家淡泊名利并付出更艰苦地努力。另一方面，我们也要从客观上为数学家创造更有利的发展数学事业的外部环境，这主要是加强对数学事业的支持与投资力度，使数学家有较好的工作与生活条件，其中也包括改善与加强数学的出版工作。 这次科学出版社购买了版权，一次影印了23本施普林格出版社出版的数学书，就是一件好事，也是值得继续做下去的事情。大体上分一下，这23本书中，包括基础数学书5本，应用数学书6本与计算数学书12本，其中有些也具有交叉性质。 这些书可以使读者较快地了解数学某方面的前沿，对从事这方面研究的数学家了解该领域的前沿与全貌也很有帮助。 |
| Preface to the Second Edition Preface to the First Edition 1 Background in Linear Algebra 1.1 Matrices 1.2 Square Matrices and Eigenvalues 1.3 Types of Matrices 1.4 Vector Inner Products and Norms 1.5 Matrix Norms 1.6 Subspaces, Range, and Kernel 1.7 Orthogonal Vectors and Subspaces 1.8 Canonical Forms of Matrices 1.8.1 Reduction to the Diagonal Form 1.8.2 The Jordan Canonical Form 1.8.3 The Schur Canonical Form 1.8.4 Application to Powers of Matrices 1.9 Normal and Hermitian Matrices 1.9.1 Normal Matrices 1.9.2 Hermitian Matrices 1.10 Nonnegative Matrices, M-Matrices 1.11 Positive Definite Matrices 1.12 Projection Operators 1.12.1 Range and Null Space of a Projector 1.12.2 Matrix Representations 1.12.3 Orthogonal and Oblique Projectors 1.12.4 Properties of Orthogonal Projectors 1.13 Basic Concepts in Linear Systems 1.13.1 Existence of a Solution 1.13.2 Perturbation Analysis Exercises Notes and References 2 Discretization of Partial Differential Equations 2.1 Partial Differential Equations 2.1.1 Elliptic Operators 2.1.2 The Convection Diffusion Equation 2.2 Finite Difference Methods 2.2.1 Basic Approximations 2.2.2 Difference Schemes for the Laplacian Operator 2.2.3 Finite Differences for One-Dimensional Problems 2.2.4 Upwind Schemes 2.2.5 Finite Differences for Two-Dimensional Problems 2.2.6 Fast Poisson Solvers 2.3 The Finite Element Method 2.4 Mesh Generation and Refinement 2.5 Finite Volume Method Exercises Notes and References 3 Sparse Matrices 3.1 Introduction …… 4 Basic Iterative Methods 5 Projection Methods 6 Krylov Subspace Methods, Part Ⅰ 7 Krylov Subspace Methods, Part Ⅱ 8 Methods Related to the Normal Equations 9 Preconditioned Iterations 10 Preconditioning Techniques 11 Parallel Implementations 12 Parallel Preconditioners 13 Multigrid Methods 14 Domain Decomposition Methods Bibliography Index |
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