Rectangular eigenvalue problems
Often the easiest way to discretize an ordinary or partial differential equation is by a <i>rectangular numerical method</i>, in which <i>n</i> basis functions are sampled at <i>m</i> ≫ <i>n</i> collocation points. We show how eigenvalue problems can b...
| Main Authors: | , , |
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| Format: | Journal article |
| Language: | English |
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Springer
2022
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| _version_ | 1826309844518305792 |
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| author | Hashemi, B Nakatsukasa, Y Trefethen, LN |
| author_facet | Hashemi, B Nakatsukasa, Y Trefethen, LN |
| author_sort | Hashemi, B |
| collection | OXFORD |
| description | Often the easiest way to discretize an ordinary or partial differential equation is by a <i>rectangular numerical method</i>, in which <i>n</i> basis functions are sampled at <i>m</i> ≫ <i>n</i> collocation points. We show how eigenvalue problems can be solved in this setting by QR reduction to square matrix generalized eigenvalue problems. The method applies equally in the limit “<i>m</i> = ∞” of eigenvalue problems for quasimatrices. Numerical examples are presented as well as pointers to related literature. |
| first_indexed | 2024-03-07T07:41:45Z |
| format | Journal article |
| id | oxford-uuid:f7e8427d-ab81-47fe-9781-c8b612c24524 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T07:41:45Z |
| publishDate | 2022 |
| publisher | Springer |
| record_format | dspace |
| spelling | oxford-uuid:f7e8427d-ab81-47fe-9781-c8b612c245242023-04-26T13:59:13ZRectangular eigenvalue problemsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:f7e8427d-ab81-47fe-9781-c8b612c24524EnglishSymplectic ElementsSpringer2022Hashemi, BNakatsukasa, YTrefethen, LNOften the easiest way to discretize an ordinary or partial differential equation is by a <i>rectangular numerical method</i>, in which <i>n</i> basis functions are sampled at <i>m</i> ≫ <i>n</i> collocation points. We show how eigenvalue problems can be solved in this setting by QR reduction to square matrix generalized eigenvalue problems. The method applies equally in the limit “<i>m</i> = ∞” of eigenvalue problems for quasimatrices. Numerical examples are presented as well as pointers to related literature. |
| spellingShingle | Hashemi, B Nakatsukasa, Y Trefethen, LN Rectangular eigenvalue problems |
| title | Rectangular eigenvalue problems |
| title_full | Rectangular eigenvalue problems |
| title_fullStr | Rectangular eigenvalue problems |
| title_full_unstemmed | Rectangular eigenvalue problems |
| title_short | Rectangular eigenvalue problems |
| title_sort | rectangular eigenvalue problems |
| work_keys_str_mv | AT hashemib rectangulareigenvalueproblems AT nakatsukasay rectangulareigenvalueproblems AT trefethenln rectangulareigenvalueproblems |