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<TABLE CELLSPACING=0 CELLPADDING=0><TR><TD>Preface</TD><TD WIDTH=40></TD><TD VALIGN=TOP>ix</TD><TD></TD></TR><TR><TD>Acknowledgments</TD><TD WIDTH=40></TD><TD VALIGN=TOP>xi</TD><TD></TD></TR><TR><TD>I Fundamentals</TD><TD WIDTH=40></TD><TD VALIGN=TOP>1</TD><TD VALIGN=TOP>(38)</TD></TR><TR><TD><TABLE CELLSPACING=0 CELLPADDING=0><TR><TD WIDTH=20></TD><TD>Matrix-Vector Multiplication</TD></TR></TABLE></TD><TD WIDTH=40></TD><TD VALIGN=TOP>3</TD><TD VALIGN=TOP>(8)</TD></TR><TR><TD><TABLE CELLSPACING=0 CELLPADDING=0><TR><TD WIDTH=20></TD><TD>Orthogonal Vectors and Matrices</TD></TR></TABLE></TD><TD WIDTH=40></TD><TD VALIGN=TOP>11</TD><TD VALIGN=TOP>(6)</TD></TR><TR><TD><TABLE CELLSPACING=0 CELLPADDING=0><TR><TD WIDTH=20></TD><TD>Norms</TD></TR></TABLE></TD><TD WIDTH=40></TD><TD VALIGN=TOP>17</TD><TD VALIGN=TOP>(8)</TD></TR><TR><TD><TABLE CELLSPACING=0 CELLPADDING=0><TR><TD WIDTH=20></TD><TD>The Singular Value Decomposition</TD></TR></TABLE></TD><TD WIDTH=40></TD><TD VALIGN=TOP>25</TD><TD VALIGN=TOP>(7)</TD></TR><TR><TD><TABLE CELLSPACING=0 CELLPADDING=0><TR><TD WIDTH=20></TD><TD>More on the SVD</TD></TR></TABLE></TD><TD WIDTH=40></TD><TD VALIGN=TOP>32</TD><TD VALIGN=TOP>(7)</TD></TR><TR><TD>II QR Factorization and Least Squares</TD><TD WIDTH=40></TD><TD VALIGN=TOP>39</TD><TD VALIGN=TOP>(48)</TD></TR><TR><TD><TABLE CELLSPACING=0 CELLPADDING=0><TR><TD WIDTH=20></TD><TD>Projectors</TD></TR></TABLE></TD><TD WIDTH=40></TD><TD VALIGN=TOP>41</TD><TD VALIGN=TOP>(7)</TD></TR><TR><TD><TABLE CELLSPACING=0 CELLPADDING=0><TR><TD WIDTH=20></TD><TD>QR Factorization</TD></TR></TABLE></TD><TD WIDTH=40></TD><TD VALIGN=TOP>48</TD><TD VALIGN=TOP>(8)</TD></TR><TR><TD><TABLE CELLSPACING=0 CELLPADDING=0><TR><TD WIDTH=20></TD><TD>Gram-Schmidt Orthogonalization</TD></TR></TABLE></TD><TD WIDTH=40></TD><TD VALIGN=TOP>56</TD><TD VALIGN=TOP>(7)</TD></TR><TR><TD><TABLE CELLSPACING=0 CELLPADDING=0><TR><TD WIDTH=20></TD><TD>MATLAB</TD></TR></TABLE></TD><TD WIDTH=40></TD><TD VALIGN=TOP>63</TD><TD VALIGN=TOP>(6)</TD></TR><TR><TD><TABLE CELLSPACING=0 CELLPADDING=0><TR><TD WIDTH=20></TD><TD>Householder Triangularization</TD></TR></TABLE></TD><TD WIDTH=40></TD><TD VALIGN=TOP>69</TD><TD VALIGN=TOP>(8)</TD></TR><TR><TD><TABLE CELLSPACING=0 CELLPADDING=0><TR><TD WIDTH=20></TD><TD>Least Squares Problems</TD></TR></TABLE></TD><TD WIDTH=40></TD><TD VALIGN=TOP>77</TD><TD VALIGN=TOP>(10)</TD></TR><TR><TD>III Conditioning and Stability</TD><TD WIDTH=40></TD><TD VALIGN=TOP>87</TD><TD VALIGN=TOP>(58)</TD></TR><TR><TD><TABLE CELLSPACING=0 CELLPADDING=0><TR><TD WIDTH=20></TD><TD>Conditioning and Condition Numbers</TD></TR></TABLE></TD><TD WIDTH=40></TD><TD VALIGN=TOP>89</TD><TD VALIGN=TOP>(8)</TD></TR><TR><TD><TABLE CELLSPACING=0 CELLPADDING=0><TR><TD WIDTH=20></TD><TD>Floating Point Arithmetic</TD></TR></TABLE></TD><TD WIDTH=40></TD><TD VALIGN=TOP>97</TD><TD VALIGN=TOP>(5)</TD></TR><TR><TD><TABLE CELLSPACING=0 CELLPADDING=0><TR><TD WIDTH=20></TD><TD>Stability</TD></TR></TABLE></TD><TD WIDTH=40></TD><TD VALIGN=TOP>102</TD><TD VALIGN=TOP>(6)</TD></TR><TR><TD><TABLE CELLSPACING=0 CELLPADDING=0><TR><TD WIDTH=20></TD><TD>More on Stability</TD></TR></TABLE></TD><TD WIDTH=40></TD><TD VALIGN=TOP>108</TD><TD VALIGN=TOP>(6)</TD></TR><TR><TD><TABLE CELLSPACING=0 CELLPADDING=0><TR><TD WIDTH=20></TD><TD>Stability of Householder Triangularization</TD></TR></TABLE></TD><TD WIDTH=40></TD><TD VALIGN=TOP>114</TD><TD VALIGN=TOP>(7)</TD></TR><TR><TD><TABLE CELLSPACING=0 CELLPADDING=0><TR><TD WIDTH=20></TD><TD>Stability of Back Substitution</TD></TR></TABLE></TD><TD WIDTH=40></TD><TD VALIGN=TOP>121</TD><TD VALIGN=TOP>(8)</TD></TR><TR><TD><TABLE CELLSPACING=0 CELLPADDING=0><TR><TD WIDTH=20></TD><TD>Conditioning of Least Squares Problems</TD></TR></TABLE></TD><TD WIDTH=40></TD><TD VALIGN=TOP>129</TD><TD VALIGN=TOP>(8)</TD></TR><TR><TD><TABLE CELLSPACING=0 CELLPADDING=0><TR><TD WIDTH=20></TD><TD>Stability of Least Squares Algorithms</TD></TR></TABLE></TD><TD WIDTH=40></TD><TD VALIGN=TOP>137</TD><TD VALIGN=TOP>(8)</TD></TR><TR><TD>IV Systems of Equations</TD><TD WIDTH=40></TD><TD VALIGN=TOP>145</TD><TD VALIGN=TOP>(34)</TD></TR><TR><TD><TABLE CELLSPACING=0 CELLPADDING=0><TR><TD WIDTH=20></TD><TD>Gaussian Elimination</TD></TR></TABLE></TD><TD WIDTH=40></TD><TD VALIGN=TOP>147</TD><TD VALIGN=TOP>(8)</TD></TR><TR><TD><TABLE CELLSPACING=0 CELLPADDING=0><TR><TD WIDTH=20></TD><TD>Pivoting</TD></TR></TABLE></TD><TD WIDTH=40></TD><TD VALIGN=TOP>155</TD><TD VALIGN=TOP>(8)</TD></TR><TR><TD><TABLE CELLSPACING=0 CELLPADDING=0><TR><TD WIDTH=20></TD><TD>Stability of Gaussian Elimination</TD></TR></TABLE></TD><TD WIDTH=40></TD><TD VALIGN=TOP>163</TD><TD VALIGN=TOP>(9)</TD></TR><TR><TD><TABLE CELLSPACING=0 CELLPADDING=0><TR><TD WIDTH=20></TD><TD>Cholesky Factorization</TD></TR></TABLE></TD><TD WIDTH=40></TD><TD VALIGN=TOP>172</TD><TD VALIGN=TOP>(7)</TD></TR><TR><TD>V Eigenvalues</TD><TD WIDTH=40></TD><TD VALIGN=TOP>179</TD><TD VALIGN=TOP>(62)</TD></TR><TR><TD><TABLE CELLSPACING=0 CELLPADDING=0><TR><TD WIDTH=20></TD><TD>Eigenvalue Problems</TD></TR></TABLE></TD><TD WIDTH=40></TD><TD VALIGN=TOP>181</TD><TD VALIGN=TOP>(9)</TD></TR><TR><TD><TABLE CELLSPACING=0 CELLPADDING=0><TR><TD WIDTH=20></TD><TD>Overview of Eigenvalue Algorithms</TD></TR></TABLE></TD><TD WIDTH=40></TD><TD VALIGN=TOP>190</TD><TD VALIGN=TOP>(6)</TD></TR><TR><TD><TABLE CELLSPACING=0 CELLPADDING=0><TR><TD WIDTH=20></TD><TD>Reduction to Hessenberg or Tridiagonal Form</TD></TR></TABLE></TD><TD WIDTH=40></TD><TD VALIGN=TOP>196</TD><TD VALIGN=TOP>(6)</TD></TR><TR><TD><TABLE CELLSPACING=0 CELLPADDING=0><TR><TD WIDTH=20></TD><TD>Rayleigh Quotient, Inverse Iteration</TD></TR></TABLE></TD><TD WIDTH=40></TD><TD VALIGN=TOP>202</TD><TD VALIGN=TOP>(9)</TD></TR><TR><TD><TABLE CELLSPACING=0 CELLPADDING=0><TR><TD WIDTH=20></TD><TD>QR Algorithm without Shifts</TD></TR></TABLE></TD><TD WIDTH=40></TD><TD VALIGN=TOP>211</TD><TD VALIGN=TOP>(8)</TD></TR><TR><TD><TABLE CELLSPACING=0 CELLPADDING=0><TR><TD WIDTH=20></TD><TD>QR Algorithm with Shifts</TD></TR></TABLE></TD><TD WIDTH=40></TD><TD VALIGN=TOP>219</TD><TD VALIGN=TOP>(6)</TD></TR><TR><TD><TABLE CELLSPACING=0 CELLPADDING=0><TR><TD WIDTH=20></TD><TD>Other Eigenvalue Algorithms</TD></TR></TABLE></TD><TD WIDTH=40></TD><TD VALIGN=TOP>225</TD><TD VALIGN=TOP>(9)</TD></TR><TR><TD><TABLE CELLSPACING=0 CELLPADDING=0><TR><TD WIDTH=20></TD><TD>Computing the SVD</TD></TR></TABLE></TD><TD WIDTH=40></TD><TD VALIGN=TOP>234</TD><TD VALIGN=TOP>(7)</TD></TR><TR><TD>VI Iterative Methods</TD><TD WIDTH=40></TD><TD VALIGN=TOP>241</TD><TD VALIGN=TOP>(80)</TD></TR><TR><TD><TABLE CELLSPACING=0 CELLPADDING=0><TR><TD WIDTH=20></TD><TD>Overview of Iterative Methods</TD></TR></TABLE></TD><TD WIDTH=40></TD><TD VALIGN=TOP>243</TD><TD VALIGN=TOP>(7)</TD></TR><TR><TD><TABLE CELLSPACING=0 CELLPADDING=0><TR><TD WIDTH=20></TD><TD>The Arnoldi Iteration</TD></TR></TABLE></TD><TD WIDTH=40></TD><TD VALIGN=TOP>250</TD><TD VALIGN=TOP>(7)</TD></TR><TR><TD><TABLE CELLSPACING=0 CELLPADDING=0><TR><TD WIDTH=20></TD><TD>How Arnoldi Locates Eigenvalues</TD></TR></TABLE></TD><TD WIDTH=40></TD><TD VALIGN=TOP>257</TD><TD VALIGN=TOP>(9)</TD></TR><TR><TD><TABLE CELLSPACING=0 CELLPADDING=0><TR><TD WIDTH=20></TD><TD>GMRES</TD></TR></TABLE></TD><TD WIDTH=40></TD><TD VALIGN=TOP>266</TD><TD VALIGN=TOP>(10)</TD></TR><TR><TD><TABLE CELLSPACING=0 CELLPADDING=0><TR><TD WIDTH=20></TD><TD>The Lanczos Iteration</TD></TR></TABLE></TD><TD WIDTH=40></TD><TD VALIGN=TOP>276</TD><TD VALIGN=TOP>(9)</TD></TR><TR><TD><TABLE CELLSPACING=0 CELLPADDING=0><TR><TD WIDTH=20></TD><TD>From Lanczos to Gauss Quadrature</TD></TR></TABLE></TD><TD WIDTH=40></TD><TD VALIGN=TOP>285</TD><TD VALIGN=TOP>(8)</TD></TR><TR><TD><TABLE CELLSPACING=0 CELLPADDING=0><TR><TD WIDTH=20></TD><TD>Conjugate Gradients</TD></TR></TABLE></TD><TD WIDTH=40></TD><TD VALIGN=TOP>293</TD><TD VALIGN=TOP>(10)</TD></TR><TR><TD><TABLE CELLSPACING=0 CELLPADDING=0><TR><TD WIDTH=20></TD><TD>Biorthogonalization Methods</TD></TR></TABLE></TD><TD WIDTH=40></TD><TD VALIGN=TOP>303</TD><TD VALIGN=TOP>(10)</TD></TR><TR><TD><TABLE CELLSPACING=0 CELLPADDING=0><TR><TD WIDTH=20></TD><TD>Preconditioning</TD></TR></TABLE></TD><TD WIDTH=40></TD><TD VALIGN=TOP>313</TD><TD VALIGN=TOP>(8)</TD></TR><TR><TD>Appendix The Definition of Numerical Analysis</TD><TD WIDTH=40></TD><TD VALIGN=TOP>321</TD><TD VALIGN=TOP>(8)</TD></TR><TR><TD>Notes</TD><TD WIDTH=40></TD><TD VALIGN=TOP>329</TD><TD VALIGN=TOP>(14)</TD></TR><TR><TD>Bibliography</TD><TD WIDTH=40></TD><TD VALIGN=TOP>343</TD><TD VALIGN=TOP>(10)</TD></TR><TR><TD>Index</TD><TD WIDTH=40></TD><TD VALIGN=TOP>353</TD><TD></TD></TR></TABLE>

Society for Industrial and Applied Mathematics

An introduction to the field of numerical linear algebra. It aims to present the core, standard material in a novel way. Topics include iterative methods for systems of equations and eigenvalue problems and the underlying principles of conditioning and stability

Numerical linear algebra