Three steps on an open road
This note describes three recent factorizations of banded invertible infinite matrices: 1. If A has a banded inverse: A = BC with block--diagonal factors B and C. 2. Permutations factor into a shift times N<2w tridiagonal permutations. 3. A = LPU with lower triangular L, permutation P, upper tria...
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| Format: | Article |
| Language: | en_US |
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American Institute of Mathematical Sciences
2013
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| Online Access: | http://hdl.handle.net/1721.1/81407 https://orcid.org/0000-0001-7473-9287 |
| _version_ | 1826198784364773376 |
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| author | Strang, Gilbert |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Strang, Gilbert |
| author_sort | Strang, Gilbert |
| collection | MIT |
| description | This note describes three recent factorizations of banded invertible infinite matrices: 1. If A has a banded inverse: A = BC with block--diagonal factors B and C. 2. Permutations factor into a shift times N<2w tridiagonal permutations. 3. A = LPU with lower triangular L, permutation P, upper triangular U. We include examples and references and outlines of proofs. |
| first_indexed | 2024-09-23T11:09:57Z |
| format | Article |
| id | mit-1721.1/81407 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T11:09:57Z |
| publishDate | 2013 |
| publisher | American Institute of Mathematical Sciences |
| record_format | dspace |
| spelling | mit-1721.1/814072022-10-01T01:43:07Z Three steps on an open road Strang, Gilbert Massachusetts Institute of Technology. Department of Mathematics Strang, Gilbert This note describes three recent factorizations of banded invertible infinite matrices: 1. If A has a banded inverse: A = BC with block--diagonal factors B and C. 2. Permutations factor into a shift times N<2w tridiagonal permutations. 3. A = LPU with lower triangular L, permutation P, upper triangular U. We include examples and references and outlines of proofs. National Science Foundation (U.S.) (Grant 1023152) 2013-10-16T16:24:46Z 2013-10-16T16:24:46Z 2013-09 2012-12 Article http://purl.org/eprint/type/JournalArticle 1930-8337 http://hdl.handle.net/1721.1/81407 Strang, Gilbert. “Three steps on an open road.” Inverse Problems and Imaging 7, no. 3 (August 2013): 961-966. © American Institute of Mathematical Sciences https://orcid.org/0000-0001-7473-9287 en_US http://dx.doi.org/10.3934/ipi.2013.7.961 Inverse Problems and Imaging Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. application/pdf American Institute of Mathematical Sciences American Institute of Mathematical Sciences |
| spellingShingle | Strang, Gilbert Three steps on an open road |
| title | Three steps on an open road |
| title_full | Three steps on an open road |
| title_fullStr | Three steps on an open road |
| title_full_unstemmed | Three steps on an open road |
| title_short | Three steps on an open road |
| title_sort | three steps on an open road |
| url | http://hdl.handle.net/1721.1/81407 https://orcid.org/0000-0001-7473-9287 |
| work_keys_str_mv | AT stranggilbert threestepsonanopenroad |