Afternotes goes to graduate school : lectures on advanced numerical analysis : a series of lectures on advanced numerical analysis presented at the University of Maryland at College Park and recorded after the fact

In this follow-up to Afternotes on Numerical Analysis (SIAM, 1996) the author continues to bring the immediacy of the classroom to the printed page. Like the original undergraduate volume, Afternotes Goes to Graduate School is the result of the author writing down his notes immediately after giving each lecture; in this case the afternotes are the result of a follow-up graduate course taught by Professor Stewart at the University of Maryland. The algorithms presented in this volume require deeper mathematical understanding than those in the undergraduate book, and their implementations are not trivial. Stewart uses a fresh presentation that is clear and intuitive as he covers topics such as discrete and continuous approximation, linear and quadratic splines, eigensystems, and Krylov sequence methods. He concludes with two lectures on classical iterative methods and nonlinear equations. Contents......Page 6 Preface......Page 12 Approximation......Page 14 Lecture 1......Page 16 Lecture 2......Page 24 Lecture 3......Page 30 Lecture 4......Page 36 Lecture 5......Page 44 Lecture 6......Page 52 Lecture 7......Page 60 Lecture 8......Page 70 Lecture 9......Page 80 Linear and Cubic Splines......Page 92 Lecture 10......Page 94 Lecture 11......Page 106 Eigensystems......Page 116 Lecture 12......Page 118 Lecture 13......Page 128 Lecture 14......Page 138 Lecture 15......Page 148 Lecture 16......Page 158 Lecture 17......Page 164 Lecture 18......Page 170 Krylov Sequence Methods......Page 178 Lecture 19......Page 180 Lecture 20......Page 190 Lecture 21......Page 196 Lecture 22......Page 204 Lecture 23......Page 210 Lecture 24......Page 218 Iterations, Linear and Nonlinear......Page 226 Lecture 25......Page 228 Lecture 26......Page 236 Bibliography......Page 246 Index......Page 250 An overview of modern computer stabilization methods for linear inversion, with applications to a variety of problems in audio processing, medical imaging, tomography, seismology and astronomy. This book describes methods for the analysis of rank-deficient and discrete ill-posed problems G.w. Stewart. Includes Bibliographical References (p. 233-235) And Index.