Geršgorin and His Circles:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
2004
|
| Schriftenreihe: | Springer Series in Computational Mathematics
36 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | TheGer? sgorin CircleTheorem, averywell-known resultin linear algebra today, stems from the paper of S. Ger? sgorin in 1931 (which is reproduced in AppendixD)where,given an arbitraryn ×n complex matrix, easy arithmetic operations on the entries of the matrix producen disks, in the complex plane, whose union contains all eigen values of the given matrix. The beauty and simplicity of Ger? sgorin's Theorem has undoubtedly inspired further research in this area, resulting in hundreds of papers in which the name "Ger? sgorin" appears. The goal of this book is to give a careful and up-to-date treatment of various aspects of this topic. The author ?rst learned of Ger? sgorin's results from friendly conversations with Olga Taussky-Todd and John Todd, which inspired me to work in this area. Olga was clearly passion ate about linear algebra and matrix theory, and her path-?nding results in these areas were like a magnet to many, including this author! It is the author's hope that the results, presented here on topics related to Ger? sgorin's Theorem, will be of interest to many. This book is a?ectionately dedicated to my mentors, Olga Taussky-Todd and John Todd. There are two main recurring themes which the reader will see in this book. The ?rst recurring theme is that a nonsingularity theorem for a mat- ces gives rise to an equivalent eigenvalue inclusion set in the complex plane for matrices, and conversely. Though common knowledge today, this was not widely recognized until many years after Ger? sgorin's paper appeared. That these two items, nonsingularity theorems and eigenvalue inclusion sets, go hand-in-hand, will be often seen in this book. |
| Beschreibung: | 1 Online-Ressource (X, 226p. 1 illus. in color) |
| ISBN: | 9783642177989 9783540211006 |
| ISSN: | 0179-3632 |
| DOI: | 10.1007/978-3-642-17798-9 |
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| 500 | |a TheGer? sgorin CircleTheorem, averywell-known resultin linear algebra today, stems from the paper of S. Ger? sgorin in 1931 (which is reproduced in AppendixD)where,given an arbitraryn ×n complex matrix, easy arithmetic operations on the entries of the matrix producen disks, in the complex plane, whose union contains all eigen values of the given matrix. The beauty and simplicity of Ger? sgorin's Theorem has undoubtedly inspired further research in this area, resulting in hundreds of papers in which the name "Ger? sgorin" appears. The goal of this book is to give a careful and up-to-date treatment of various aspects of this topic. The author ?rst learned of Ger? sgorin's results from friendly conversations with Olga Taussky-Todd and John Todd, which inspired me to work in this area. Olga was clearly passion ate about linear algebra and matrix theory, and her path-?nding results in these areas were like a magnet to many, including this author! It is the author's hope that the results, presented here on topics related to Ger? sgorin's Theorem, will be of interest to many. This book is a?ectionately dedicated to my mentors, Olga Taussky-Todd and John Todd. There are two main recurring themes which the reader will see in this book. The ?rst recurring theme is that a nonsingularity theorem for a mat- ces gives rise to an equivalent eigenvalue inclusion set in the complex plane for matrices, and conversely. Though common knowledge today, this was not widely recognized until many years after Ger? sgorin's paper appeared. That these two items, nonsingularity theorems and eigenvalue inclusion sets, go hand-in-hand, will be often seen in this book. | ||
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Datensatz im Suchindex
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| author | Varga, Richard S. 1928-2022 |
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| author_facet | Varga, Richard S. 1928-2022 |
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| author_sort | Varga, Richard S. 1928-2022 |
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| building | Verbundindex |
| bvnumber | BV042422459 |
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| ctrlnum | (OCoLC)1184365643 (DE-599)BVBBV042422459 |
| dewey-full | 518 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 518 - Numerical analysis |
| dewey-raw | 518 |
| dewey-search | 518 |
| dewey-sort | 3518 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-642-17798-9 |
| format | Electronic eBook |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:11Z |
| institution | BVB |
| isbn | 9783642177989 9783540211006 |
| issn | 0179-3632 |
| language | English |
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| spelling | Varga, Richard S. 1928-2022 Verfasser (DE-588)1068286725 aut Geršgorin and His Circles by Richard S. Varga Berlin, Heidelberg Springer Berlin Heidelberg 2004 1 Online-Ressource (X, 226p. 1 illus. in color) txt rdacontent c rdamedia cr rdacarrier Springer Series in Computational Mathematics 36 0179-3632 TheGer? sgorin CircleTheorem, averywell-known resultin linear algebra today, stems from the paper of S. Ger? sgorin in 1931 (which is reproduced in AppendixD)where,given an arbitraryn ×n complex matrix, easy arithmetic operations on the entries of the matrix producen disks, in the complex plane, whose union contains all eigen values of the given matrix. The beauty and simplicity of Ger? sgorin's Theorem has undoubtedly inspired further research in this area, resulting in hundreds of papers in which the name "Ger? sgorin" appears. The goal of this book is to give a careful and up-to-date treatment of various aspects of this topic. The author ?rst learned of Ger? sgorin's results from friendly conversations with Olga Taussky-Todd and John Todd, which inspired me to work in this area. Olga was clearly passion ate about linear algebra and matrix theory, and her path-?nding results in these areas were like a magnet to many, including this author! It is the author's hope that the results, presented here on topics related to Ger? sgorin's Theorem, will be of interest to many. This book is a?ectionately dedicated to my mentors, Olga Taussky-Todd and John Todd. There are two main recurring themes which the reader will see in this book. The ?rst recurring theme is that a nonsingularity theorem for a mat- ces gives rise to an equivalent eigenvalue inclusion set in the complex plane for matrices, and conversely. Though common knowledge today, this was not widely recognized until many years after Ger? sgorin's paper appeared. That these two items, nonsingularity theorems and eigenvalue inclusion sets, go hand-in-hand, will be often seen in this book. Mathematics Numerical analysis Numerical Analysis Mathematik Matrizen-Eigenwertaufgabe (DE-588)4120715-4 gnd rswk-swf Komplexe Matrix (DE-588)4566051-7 gnd rswk-swf Komplexe Matrix (DE-588)4566051-7 s Matrizen-Eigenwertaufgabe (DE-588)4120715-4 s 1\p DE-604 https://doi.org/10.1007/978-3-642-17798-9 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Varga, Richard S. 1928-2022 Geršgorin and His Circles Mathematics Numerical analysis Numerical Analysis Mathematik Matrizen-Eigenwertaufgabe (DE-588)4120715-4 gnd Komplexe Matrix (DE-588)4566051-7 gnd |
| subject_GND | (DE-588)4120715-4 (DE-588)4566051-7 |
| title | Geršgorin and His Circles |
| title_auth | Geršgorin and His Circles |
| title_exact_search | Geršgorin and His Circles |
| title_full | Geršgorin and His Circles by Richard S. Varga |
| title_fullStr | Geršgorin and His Circles by Richard S. Varga |
| title_full_unstemmed | Geršgorin and His Circles by Richard S. Varga |
| title_short | Geršgorin and His Circles |
| title_sort | gersgorin and his circles |
| topic | Mathematics Numerical analysis Numerical Analysis Mathematik Matrizen-Eigenwertaufgabe (DE-588)4120715-4 gnd Komplexe Matrix (DE-588)4566051-7 gnd |
| topic_facet | Mathematics Numerical analysis Numerical Analysis Mathematik Matrizen-Eigenwertaufgabe Komplexe Matrix |
| url | https://doi.org/10.1007/978-3-642-17798-9 |
| work_keys_str_mv | AT vargarichards gersgorinandhiscircles |