LEADER 05553nam 2200685 450 001 996426340803316 005 20230120002114.0 010 $a0-12-394784-7 035 $a(CKB)3710000000240366 035 $a(EBL)1789498 035 $a(SSID)ssj0001398889 035 $a(PQKBManifestationID)11810248 035 $a(PQKBTitleCode)TC0001398889 035 $a(PQKBWorkID)11446790 035 $a(PQKB)11760947 035 $a(Au-PeEL)EBL1789498 035 $a(CaPaEBR)ebr10933356 035 $a(CaONFJC)MIL785258 035 $a(OCoLC)891671192 035 $a(CaSebORM)9780123944351 035 $a(MiAaPQ)EBC1789498 035 $a(EXLCZ)993710000000240366 100 $a20140922h20152015 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aNumerical linear algebra with applications $eusing matlab /$fby William Ford 205 $aFirst edition. 210 1$aLondon, England :$cAcademic Press,$d2015. 210 4$dİ2015 215 $a1 online resource (629 p.) 300 $aDescription based upon print version of record 311 $a0-12-394435-X 320 $aIncludes bibliographical references and index. 327 $aFront 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 327 $aApplication: 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 327 $aDiagonalizationPowers 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 Norm 327 $aInduced 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 Examples 327 $aInner 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 Problem 327 $aPerturbation Analysis for Solving a Linear System 330 $aDesigned 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 for 606 $aAlgebras, Linear$xData processing 606 $aEngineering mathematics$xData processing 608 $aProblems and exercises.$2fast 615 0$aAlgebras, Linear$xData processing. 615 0$aEngineering mathematics$xData processing. 676 $a512.5 686 $aST 601$2rvk 686 $aSK 220$2rvk 686 $aST 601 M35$2rvk 700 $aFord$b William H.$01068342 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996426340803316 996 $aNumerical linear algebra with applications$92552992 997 $aUNISA