05553nam 2200685 450 99642634080331620230120002114.00-12-394784-7(CKB)3710000000240366(EBL)1789498(SSID)ssj0001398889(PQKBManifestationID)11810248(PQKBTitleCode)TC0001398889(PQKBWorkID)11446790(PQKB)11760947(Au-PeEL)EBL1789498(CaPaEBR)ebr10933356(CaONFJC)MIL785258(OCoLC)891671192(CaSebORM)9780123944351(MiAaPQ)EBC1789498(EXLCZ)99371000000024036620140922h20152015 uy 0engur|n|---|||||txtrdacontentcrdamediacrrdacarrierNumerical linear algebra with applications using matlab /by William FordFirst edition.London, England :Academic Press,2015.©20151 online resource (629 p.)Description based upon print version of record0-12-394435-X 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 SystemsApplication: 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 EigenvectorsDiagonalizationPowers of Matrices; Applications; Electric Circuit; Irreducible Matrices; Ranking of Teams Using Eigenvectors; Computing Eigenvalues and Eigenvectors using MATLAB; 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 NormInduced Matrix NormsSubmultiplicative Matrix Norms; Computing the Matrix 2-Norm; Properties of the Matrix 2-Norm; Chapter Summary; Problems; MATLAB Problems; Floating Point 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 ExamplesInner 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 of Algorithms; Why Do We Need Numerical Linear Algebra?; Computation Error; Forward Error; Backward Error; Algorithm Stability; Examples of Unstable Algorithms; Conditioning of a ProblemPerturbation Analysis for Solving a Linear SystemDesigned 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, this book is ideal for solving real-world problems. It provides necessary mathematical background information forAlgebras, LinearData processingEngineering mathematicsData processingProblems and exercises.fastAlgebras, LinearData processing.Engineering mathematicsData processing.512.5ST 601rvkSK 220rvkST 601 M35rvkFord William H.1068342MiAaPQMiAaPQMiAaPQBOOK996426340803316Numerical linear algebra with applications2552992UNISA