Special Matrices and Their Applications in Numerical Mathematics

Name: Special Matrices and Their Applications in Numerical Mathematics | Second Edition
Brand: Dover Publications
Price: 29.49 EUR
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Second Edition

Miroslav Fiedler(Autor*in)

Dover Publications (Verlag)

Erschienen am 1. Dezember 2013

343 Seiten

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Inhalt

Title Page
Copyright Page
Contents
Preface
1 Basic Concepts of Matrix Theory
1.1 Matrices
1.2 Determinants
1.3 Nonsingular Matrices. Inverse Matrices
1.4 Schur Complement. Factorization
1.5 Vector Spaces. Rank
1.6 Eigenvectors, Eigenvalues. Characteristic Polynomial
1.7 Similarity. Jordan Normal Form
2 Symmetric Matrices. Positive Definite and Semidefinite Matrices
2.1 Euclidean and Unitary Spaces
2.2 Symmetric and Hermitian Matrices
2.3 Orthogonal, Unitary Matrices
2.4 Gram-Schmidt Orthonormalization
2.5 Positive Definite Matrices
2.6 Sylvester's Law of Inertia
2.7 Singular Value Decomposition
3 Graphs and Matrices
3.1 Digraphs
3.2 Digraph of a Matrix
3.3 Undirected Graphs. Trees
3.4 Bigraphs
4 Nonnegative Matrices. Stochastic and Doubly Stochastic Matrices
4.1 Nonnegative matrices
4.2 The Perron-Frobenius Theorem
4.3 Cyclic Matrices
4.4 Stochastic Matrices
4.5 Doubly Stochastic Matrices
5 M-Matrices (Matrices of Classes K and K0)
5.1 Class K
5.2 Class K0
5.3 Diagonally Dominant matrices
5.4 Monotone Matrices
5.5 Class P
6 Tensor Product of Matrices. Compound Matrices
6.1 Tensor Product
6.2 Compound Matrices
7 Matrices and Polynomials. Stable Matrices
7.1 Characteristic Polynomial
7.2 Matrices Associated with Polynomials
7.3 Bézout Matrices
7.4 Hankel Matrices.
7.5 Toeplitz and Löwner Matrices
7.6 Stable Matrices
8 Band Matrices
8.1 Band Matrices and Graphs
8.2 Eigenvalues and Eigenvectors of Tridiagonal Matrices
9 Norms and Their Use for Estimation of Eigenvalues
9.1 Norms
9.2 Measure of Nonsingularity. Dual Norms
9.3 Bounds for Eigenvalues
10 Direct Methods for Solving Linear Systems
10.1 Nonsingular Case
10.2 General Case
11 Iterative Methods for Solving Linear Systems
11.1 General Case
11.2 The Jacobi Method
11.3 The Gauss-Seidel Method
11.4 The SOR Method
12 Matrix Inversion
12.1 Inversion of Special Matrices
12.2 The Pseudoinverse
13 Numerical Methods for Computing Eigenvalues of Matrices
13.1 Computation of Selected Eigenvalues
13.2 Computation of all the Eigenvalues
14 Sparse Matrices
14.1 Storing. Elimination Ordering
14.2 Envelopes. Profile
Bibliography
Index

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