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[ author_sort:"ford, william." ]
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Numerical Linear Algebra with Applic...
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Ford, William.
Numerical Linear Algebra with ApplicationsUsing MATLAB /
紀錄類型:
書目-電子資源 : Monograph/item
正題名/作者:
Numerical Linear Algebra with ApplicationsWilliam Ford.
其他題名:
Using MATLAB /
作者:
Ford, William.
出版者:
London :Academic Press,2014.
面頁冊數:
1 online resource (629 p.)
附註:
Description based upon print version of record.
附註:
Perturbation Analysis for Solving a Linear System.
標題:
Algebras, Linear.
電子資源:
click for full text
ISBN:
9780123947840 (electronic bk.)
Numerical Linear Algebra with ApplicationsUsing MATLAB /
Ford, William.
Numerical Linear Algebra with Applications
Using MATLAB /[electronic resource] :William Ford. - 1st ed. - London :Academic Press,2014. - 1 online resource (629 p.)
Description based upon print version of record.
Includes bibliographical references and index.
Front Cover; Numerical Linear Algebra with Applications; Copyright; Dedication; Contents; List of Figures; List of Algorithms; Preface; Matrices; Matrix Arithmetic; Matrix Product; The Trace; MATLAB Examples; Linear Transformations; Rotations; Powers of Matrices; Nonsingular Matrices; The Matrix Transpose and Symmetric Matrices; Chapter Summary; Problems; MATLAB Problems; Linear Equations; Introduction to Linear Equations; Solving Square Linear Systems; Gaussian Elimination; Upper-Triangular Form; Systematic Solution of Linear Systems; Computing the Inverse; Homogeneous Systems
Designed for those who want to gain a practical knowledge of modern computational techniques for the numerical solution of linear algebra problems, Numerical Linear Algebra with Applications contains all the material necessary for a first year graduate or advanced undergraduate course on numerical linear algebra with numerous applications to engineering and science. With a unified presentation of computation, basic algorithm analysis, and numerical methods to compute solutions, thisbook is ideal for solving real-world problems. It providesnecessary mathematical background information for.
ISBN: 9780123947840 (electronic bk.)Subjects--Topical Terms:
183087
Algebras, Linear.
Index Terms--Genre/Form:
214472
Electronic books.
LC Class. No.: QA184
Dewey Class. No.: 512
Numerical Linear Algebra with ApplicationsUsing MATLAB /
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Application: A TrussApplication: Electrical Circuit; Chapter Summary; Problems; MATLAB Problems; Subspaces; Introduction; Subspaces of Rn; Linear Independence; Basis of a Subspace; The Rank of a Matrix; Chapter Summary; Problems; MATLAB Problems; Determinants; Developing the Determinant of a 2bold0mu mumu section2 and a 3bold0mu mumu section3 Matrix; Expansion by Minors; Computing a Determinant Using Row Operations; Application: Encryption;Chapter Summary; Problems; MATLAB Problems; Eigenvalues and Eigenvectors; Definitions and Examples; Selected Properties of Eigenvalues and Eigenvectors
505
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DiagonalizationPowers of Matrices; Applications; Electric Circuit; Irreducible Matrices; Ranking of Teams Using Eigenvectors; Computing Eigenvalues and Eigenvectors usingMATLAB; Chapter Summary; Problems; MATLAB Problems; Orthogonal Vectors and Matrices; Introduction; The Inner Product; Orthogonal Matrices; Symmetric Matrices and Orthogonality; The L2 Inner Product; The Cauchy-Schwarz Inequality; Signal Comparison; Chapter Summary; Problems; MATLAB Problems; Vector and Matrix Norms; Vector Norms; Properties of the 2-Norm; Spherical Coordinates; Matrix Norms; The Frobenius Matrix Norm
505
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Induced Matrix NormsSubmultiplicative Matrix Norms; Computing the Matrix 2-Norm; Properties of the Matrix 2-Norm; Chapter Summary; Problems; MATLAB Problems; FloatingPoint Arithmetic; Integer Representation; Floating-Point Representation; Mapping from Real Numbers to Floating-Point Numbers; Floating-Point Arithmetic; Relative Error; Rounding Error Bounds; Addition; Multiplication; Matrix Operations; Minimizing Errors; Avoid Adding a Huge Number to a Small Number; Avoid Subtracting Numbers That Are Close; Chapter Summary; Problems; MATLAB Problems; Algorithms; Pseudocode Examples
505
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Inner Product of Two VectorsComputing the Frobenius Norm; Matrix Multiplication; Block Matrices; Algorithm Efficiency; Smaller Flop Count Is Not Always Better; Measuring Truncation Error; The Solution to Upper and Lower Triangular Systems; Efficiency Analysis; The Thomas Algorithm; Efficiency Analysis; Chapter Summary; Problems;MATLAB Problems; Conditioning of Problems and Stability ofAlgorithms; Why Do We Need Numerical Linear Algebra?; Computation Error; Forward Error; Backward Error; Algorithm Stability; Examples of Unstable Algorithms; Conditioning of a Problem
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click for full text
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