Conjugate Direction Methods in Optimization:
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
New York, NY
Springer New York
1980
|
| Series: | Applications of Mathematics
12 |
| Subjects: | |
| Online Access: | Volltext |
| Item Description: | Shortly after the end of World War II high-speed digital computing machines were being developed. It was clear that the mathematical aspects of com putation needed to be reexamined in order to make efficient use of high-speed digital computers for mathematical computations. Accordingly, under the leadership of Min a Rees, John Curtiss, and others, an Institute for Numerical Analysis was set up at the University of California at Los Angeles under the sponsorship of the National Bureau of Standards. A similar institute was formed at the National Bureau of Standards in Washington, D. C. In 1949 J. Barkeley Rosser became Director of the group at UCLA for a period of two years. During this period we organized a seminar on the study of solutions of simultaneous linear equations and on the determination of eigenvalues. G. Forsythe, W. Karush, C. Lanczos, T. Motzkin, L. J. Paige, and others attended this seminar. We discovered, for example, that even Gaussian elimination was not well understood from a machine point of view and that no effective machine oriented elimination algorithm had been developed. During this period Lanczos developed his three-term relationship and I had the good fortune of suggesting the method of conjugate gradients. We discovered afterward that the basic ideas underlying the two procedures are essentially the same. The concept of conjugacy was not new to me. In a joint paper with G. D. |
| Physical Description: | 1 Online-Ressource (X, 325 p) |
| ISBN: | 9781461260486 9781461260509 |
| ISSN: | 0172-4568 |
| DOI: | 10.1007/978-1-4612-6048-6 |
Staff View
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Record in the Search Index
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| isbn | 9781461260486 9781461260509 |
| issn | 0172-4568 |
| language | English |
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| spelling | Hestenes, Magnus Rudolph Verfasser aut Conjugate Direction Methods in Optimization by Magnus Rudolph Hestenes New York, NY Springer New York 1980 1 Online-Ressource (X, 325 p) txt rdacontent c rdamedia cr rdacarrier Applications of Mathematics 12 0172-4568 Shortly after the end of World War II high-speed digital computing machines were being developed. It was clear that the mathematical aspects of com putation needed to be reexamined in order to make efficient use of high-speed digital computers for mathematical computations. Accordingly, under the leadership of Min a Rees, John Curtiss, and others, an Institute for Numerical Analysis was set up at the University of California at Los Angeles under the sponsorship of the National Bureau of Standards. A similar institute was formed at the National Bureau of Standards in Washington, D. C. In 1949 J. Barkeley Rosser became Director of the group at UCLA for a period of two years. During this period we organized a seminar on the study of solutions of simultaneous linear equations and on the determination of eigenvalues. G. Forsythe, W. Karush, C. Lanczos, T. Motzkin, L. J. Paige, and others attended this seminar. We discovered, for example, that even Gaussian elimination was not well understood from a machine point of view and that no effective machine oriented elimination algorithm had been developed. During this period Lanczos developed his three-term relationship and I had the good fortune of suggesting the method of conjugate gradients. We discovered afterward that the basic ideas underlying the two procedures are essentially the same. The concept of conjugacy was not new to me. In a joint paper with G. D. Mathematics Systems theory Mathematical optimization Systems Theory, Control Calculus of Variations and Optimal Control; Optimization Mathematik Optimierung (DE-588)4043664-0 gnd rswk-swf Gradientenverfahren (DE-588)4157995-1 gnd rswk-swf Quasi-Newton-Verfahren (DE-588)4479204-9 gnd rswk-swf Quasi-Newton-Verfahren (DE-588)4479204-9 s Gradientenverfahren (DE-588)4157995-1 s Optimierung (DE-588)4043664-0 s 1\p DE-604 Applications of Mathematics 12 (DE-604)BV000895226 12 https://doi.org/10.1007/978-1-4612-6048-6 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Hestenes, Magnus Rudolph Conjugate Direction Methods in Optimization Applications of Mathematics Mathematics Systems theory Mathematical optimization Systems Theory, Control Calculus of Variations and Optimal Control; Optimization Mathematik Optimierung (DE-588)4043664-0 gnd Gradientenverfahren (DE-588)4157995-1 gnd Quasi-Newton-Verfahren (DE-588)4479204-9 gnd |
| subject_GND | (DE-588)4043664-0 (DE-588)4157995-1 (DE-588)4479204-9 |
| title | Conjugate Direction Methods in Optimization |
| title_auth | Conjugate Direction Methods in Optimization |
| title_exact_search | Conjugate Direction Methods in Optimization |
| title_full | Conjugate Direction Methods in Optimization by Magnus Rudolph Hestenes |
| title_fullStr | Conjugate Direction Methods in Optimization by Magnus Rudolph Hestenes |
| title_full_unstemmed | Conjugate Direction Methods in Optimization by Magnus Rudolph Hestenes |
| title_short | Conjugate Direction Methods in Optimization |
| title_sort | conjugate direction methods in optimization |
| topic | Mathematics Systems theory Mathematical optimization Systems Theory, Control Calculus of Variations and Optimal Control; Optimization Mathematik Optimierung (DE-588)4043664-0 gnd Gradientenverfahren (DE-588)4157995-1 gnd Quasi-Newton-Verfahren (DE-588)4479204-9 gnd |
| topic_facet | Mathematics Systems theory Mathematical optimization Systems Theory, Control Calculus of Variations and Optimal Control; Optimization Mathematik Optimierung Gradientenverfahren Quasi-Newton-Verfahren |
| url | https://doi.org/10.1007/978-1-4612-6048-6 |
| volume_link | (DE-604)BV000895226 |
| work_keys_str_mv | AT hestenesmagnusrudolph conjugatedirectionmethodsinoptimization |