Matrix algorithms in MATLAB� /

Matrix Algorithms in MATLAB focuses on the MATLAB code implementations of matrix algorithms. The MATLAB codes presented in the book are tested with thousands of runs of MATLAB randomly generated matrices, and the notation in the book follows the MATLAB style to ensure a smooth transition from formul...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Routh, Ong U. (Autor)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: London : Academic Press, an imprint of Elsevier, [2016]
Temas:
MATLAB.
MATLAB
Matrices.
Algorithms.
Computer algorithms.
Algorithmes.
algorithms.
MATHEMATICS > Algebra > Intermediate.
Computer algorithms
Algorithms
Matrices
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Matrix Algorithms in MATLAB
  • Copyright
  • Table of Contents
  • List of Figures
  • List of Figures
  • Preface
  • License Terms
  • 1 Introduction
  • Introduction
  • 1.1 Elements of Linear Algebra
  • 1.1.1 Definitions
  • 1.1.2 Linear Independence and Related Concepts
  • 1.1.3 Solution of Linear Equations
  • 1.1.4 Solution of Eigenvalue Problem
  • 1.2 A Brief Introduction of MATLAB
  • 1.3 Types of Matrices
  • 1.3.1 Square vs. Non-Square Matrices
  • 1.3.2 Symmetric vs. Non-Symmetric Matrices
  • 1.3.3 Full Rank vs. Deficient Rank Matrices
  • 1.3.4 Singular vs. Non-Singular Matrices.
  • 1.3.5 Orthogonal vs. Non-Orthogonal Matrices
  • 1.3.6 Defective vs. Non-Defective Matrices
  • 1.3.7 Positive (semi- )Definite vs. Positive Indefinite Matrices
  • 1.3.8 Zero Structured vs. Full Matrices
  • 1.4 Overview of Matrix Computations
  • 1.5 Reordering of Sparse Matrices
  • 1.6 Utility Codes
  • 2 Direct Algorithms of Decompositions of Matrices by Non-Orthogonal Transformations
  • Introduction
  • 2.1 Gauss Elimination Matrix
  • 2.2 LU Decomposition
  • 2.2.1 LU Decomposition by Gauss Elimination
  • 2.2.2 LU Decomposition by Crout Procedure
  • 2.2.3 Driver of LU Decomposition.
  • 2.2.4 LU Decomposition of an Upper Hessenberg Matrix
  • 2.2.5 LU Decomposition of a Band Matrix
  • 2.3 LDU Decomposition
  • 2.3.1 LDU Decomposition by Gauss Elimination
  • 2.3.2 LDU Decomposition by Crout Procedure
  • 2.3.3 Driver of LDU Decomposition
  • 2.4 Congruent Decomposition Algorithms for Symmetric Matrices
  • 2.4.1 Reduction of Symmetric Matrix to Diagonal (LDLt)
  • 2.4.2 Cholesky Decomposition (LLt)
  • 2.4.3 Reduction of Symmetric Matrix to Tri-Diagonal (LTLt)
  • 2.4.4 Reduction of Symmetric Matrix to Block Diagonal (LBLt)
  • 2.4.5 Modified Cholesky Decomposition (xLLt).
  • 2.5 Similarity Decomposition Algorithms
  • 2.5.1 Reduction of Square Matrix to Hessenberg by Gauss Elimination
  • 2.5.2 Reduction of Square Matrix to Tri-Diagonal by Gauss Elimination
  • 2.5.3 Reduction of Square Matrix to Tri-Diagonal by Lanczos Procedure
  • 2.6 Reduction of a Symmetric Matrix to Tri-Diagonal and Another Symmetric Matrix to Diagonal of 1s and 0s
  • 2.6.1 Hyper Rotation and Hyper Reflection
  • 2.6.2 GTJGt Decomposition by Hyperbolic Rotation or Hyperbolic Reflection
  • 3 Direct Algorithms of Decompositions of Matrices by Orthogonal Transformations
  • Introduction.
  • 3.1 Householder Reflection Matrix and Givens Rotation Matrix
  • 3.2 QR Decomposition
  • 3.2.1 QR Decomposition by Householder Reflections
  • 3.2.2 QR Decomposition by Givens Rotations
  • 3.2.3 QR Decomposition by Gram
  • Schmidt Orthogonalizations
  • 3.2.4 Driver of QR Decomposition
  • 3.2.5 QR Decomposition of an Upper Hessenberg Matrix
  • 3.2.6 QR Decomposition of a Band Matrix
  • 3.3 Complete Orthogonal Decomposition (QLZ)
  • 3.4 Reduction of Matrix to Bi-Diagonal
  • 3.4.1 QBZ Decomposition by Householder Reflections
  • 3.4.2 QBZ Decomposition by Givens Rotations.
  • 3.4.3 QBZ Decomposition by Golub
  • Kahan
  • Lanczos Procedure.

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