Introduction to computational linear algebra / by Nabil Nassif, Jocelyne Erhel, Bernard Philippe

By:

Nassif, Nabil [author]

Contributor(s):

Material type: Text

TextLanguage: English Publisher: Boca Raton : CRC Press, Taylor & Francis Group, [2015]Description: xxiii, 235 pages : illustrations ; 24 cmContent type:

text

Media type:

unmediated

Carrier type:

volume

ISBN:

9781482258691 (hardcover : acidfree paper)

Other title:

Computational linear algebra

Subject(s):

Algebras, Linear -- Textbooks

LOC classification:

QA184.2 N18 2015

Online resources:

View table of contents

Contents:

Basic Linear Algebra Subprograms: BLAS An Introductory Example Matrix Notations IEEE Floating Point Systems and Computer Arithmetic Vector-Vector Operations: Level-1 BLAS Matrix-Vector Operations: Level-2 BLAS Matrix-Matrix Operations: Level-3 BLAS Sparse Matrices: Storage and Associated Operations Basic Concepts for Matrix Computations Vector Norms Complements on Square Matrices Rectangular Matrices: Ranks and Singular Values Matrix Norms Gauss Elimination and LU Decompositions of Matrices Special Matrices for LU Decomposition Gauss Transforms Naive LU Decomposition for a Square Matrix with Principal Minor Property (pmp) Gauss Reduction with Partial Pivoting: PLU Decompositions MATLAB Commands Related to the LU Decomposition Condition Number of a Square Matrix Orthogonal Factorizations and Linear Least Squares Problems Formulation of Least Squares Problems: Regression Analysis Existence of Solutions Using Quadratic Forms Existence of Solutions through Matrix Pseudo-Inverse The QR Factorization Theorem Gram-Schmidt Orthogonalization: Classical, Modified, and Block Solving the Least Squares Problem with the QR Decomposition Householder QR with Column Pivoting MATLAB Implementations Algorithms for the Eigenvalue Problem Basic Principles QR Method for a Non-Symmetric Matrix Algorithms for Symmetric Matrices Methods for Large Size Matrices Singular Value Decomposition Iterative Methods for Systems of Linear Equations Stationary Methods Krylov Methods Method of Steepest Descent for spd Matrices Conjugate Gradient Method (CG) for spd Matrices The Generalized Minimal Residual Method The Bi-Conjugate Gradient Method Preconditioning Issues Sparse Systems to Solve Poisson Differential Equations Poisson Differential Equations The Path to Poisson Solvers Finite Differences for Poisson-Dirichlet Problems Variational Formulations One-Dimensional Finite-Element Discretizations Bibliography Index Exercises and Computer Exercises appear at the end of each chapter.

Summary: Introduction to Computational Linear Algebra presents classroom-tested material on computational linear algebra and its application to numerical solutions of partial and ordinary differential equations. The book is designed for senior undergraduate students in mathematics and engineering as well as first-year graduate students in engineering and computational science. The text first introduces BLAS operations of types 1, 2, and 3 adapted to a scientific computer environment, specifically MATLAB(R). It next covers the basic mathematical tools needed in numerical linear algebra and discusses classical material on Gauss decompositions as well as LU and Cholesky's factorizations of matrices. The text then shows how to solve linear least squares problems, provides a detailed numerical treatment of the algebraic eigenvalue problem, and discusses (indirect) iterative methods to solve a system of linear equations. The final chapter illustrates how to solve discretized sparse systems of linear equations. Each chapter ends with exercises and computer projects.

List(s) this item appears in: Print Books 2020

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Holdings ( 1 )
Title notes ( 5 )

Holdings
Item type	Current library	Collection	Call number	Materials specified	Status	Notes	Date due	Barcode
Books	Ladislao N. Diwa Memorial Library Reserve Section	Non-fiction	RUS QA184.2 N18 2015 (Browse shelf(Opens below))		Room use only	76421		00076329

"A Chapman & Hall book."

Includes bibliographical references and index.

Basic Linear Algebra Subprograms: BLAS
An Introductory Example
Matrix Notations
IEEE Floating Point Systems and Computer Arithmetic
Vector-Vector Operations: Level-1 BLAS
Matrix-Vector Operations: Level-2 BLAS
Matrix-Matrix Operations: Level-3 BLAS
Sparse Matrices: Storage and Associated Operations

Basic Concepts for Matrix Computations
Vector Norms
Complements on Square Matrices
Rectangular Matrices: Ranks and Singular Values
Matrix Norms

Gauss Elimination and LU Decompositions of Matrices
Special Matrices for LU Decomposition
Gauss Transforms
Naive LU Decomposition for a Square Matrix with Principal Minor Property (pmp)
Gauss Reduction with Partial Pivoting: PLU Decompositions
MATLAB Commands Related to the LU Decomposition
Condition Number of a Square Matrix

Orthogonal Factorizations and Linear Least Squares Problems
Formulation of Least Squares Problems: Regression Analysis
Existence of Solutions Using Quadratic Forms
Existence of Solutions through Matrix Pseudo-Inverse
The QR Factorization Theorem
Gram-Schmidt Orthogonalization: Classical, Modified, and Block
Solving the Least Squares Problem with the QR Decomposition
Householder QR with Column Pivoting
MATLAB Implementations

Algorithms for the Eigenvalue Problem
Basic Principles
QR Method for a Non-Symmetric Matrix
Algorithms for Symmetric Matrices
Methods for Large Size Matrices
Singular Value Decomposition

Iterative Methods for Systems of Linear Equations
Stationary Methods
Krylov Methods
Method of Steepest Descent for spd Matrices
Conjugate Gradient Method (CG) for spd Matrices
The Generalized Minimal Residual Method
The Bi-Conjugate Gradient Method
Preconditioning Issues

Sparse Systems to Solve Poisson Differential Equations
Poisson Differential Equations
The Path to Poisson Solvers
Finite Differences for Poisson-Dirichlet Problems
Variational Formulations
One-Dimensional Finite-Element Discretizations

Bibliography

Index

Exercises and Computer Exercises appear at the end of each chapter.

Introduction to Computational Linear Algebra presents classroom-tested material on computational linear algebra and its application to numerical solutions of partial and ordinary differential equations. The book is designed for senior undergraduate students in mathematics and engineering as well as first-year graduate students in engineering and computational science.

The text first introduces BLAS operations of types 1, 2, and 3 adapted to a scientific computer environment, specifically MATLAB(R). It next covers the basic mathematical tools needed in numerical linear algebra and discusses classical material on Gauss decompositions as well as LU and Cholesky's factorizations of matrices. The text then shows how to solve linear least squares problems, provides a detailed numerical treatment of the algebraic eigenvalue problem, and discusses (indirect) iterative methods to solve a system of linear equations. The final chapter illustrates how to solve discretized sparse systems of linear equations. Each chapter ends with exercises and computer projects.

Fund 164 F&J de Jesus, Inc. Purchased April 23, 2018 76421 NEJ PHP 7,267.00 2018-02-0161 2018-1-0101