Fast transforms: Banded matrices with banded inverses
It is unusual for both A and A[superscript -1] to be banded—but this can be a valuable property in applications. Block-diagonal matrices F are the simplest examples; wavelet transforms are more subtle. We show that every example can be factored into A = F[subscript 1]…F[subscript N] where N is contr...
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| Format: | Article |
| Language: | en_US |
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National Academy of Sciences (U.S.)
2013
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| Online Access: | http://hdl.handle.net/1721.1/80880 https://orcid.org/0000-0001-7473-9287 |
| _version_ | 1826198140646064128 |
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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 | It is unusual for both A and A[superscript -1] to be banded—but this can be a valuable property in applications. Block-diagonal matrices F are the simplest examples; wavelet transforms are more subtle. We show that every example can be factored into A = F[subscript 1]…F[subscript N] where N is controlled by the bandwidths of A and A[superscript -1} (but not by their size, so this extends to infinite matrices and leads to new matrix groups). |
| first_indexed | 2024-09-23T10:59:38Z |
| format | Article |
| id | mit-1721.1/80880 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T10:59:38Z |
| publishDate | 2013 |
| publisher | National Academy of Sciences (U.S.) |
| record_format | dspace |
| spelling | mit-1721.1/808802022-10-01T00:26:14Z Fast transforms: Banded matrices with banded inverses Strang, Gilbert Massachusetts Institute of Technology. Department of Mathematics Strang, Gilbert It is unusual for both A and A[superscript -1] to be banded—but this can be a valuable property in applications. Block-diagonal matrices F are the simplest examples; wavelet transforms are more subtle. We show that every example can be factored into A = F[subscript 1]…F[subscript N] where N is controlled by the bandwidths of A and A[superscript -1} (but not by their size, so this extends to infinite matrices and leads to new matrix groups). 2013-09-23T18:37:23Z 2013-09-23T18:37:23Z 2010-06 2010-03 Article http://purl.org/eprint/type/JournalArticle 0027-8424 1091-6490 http://hdl.handle.net/1721.1/80880 Strang, G. “Inaugural Article: Fast transforms: Banded matrices with banded inverses.” Proceedings of the National Academy of Sciences 107, no. 28 (July 13, 2010): 12413-12416. https://orcid.org/0000-0001-7473-9287 en_US http://dx.doi.org/10.1073/pnas.1005493107 Proceedings of the National Academy of Sciences 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 National Academy of Sciences (U.S.) PNAS |
| spellingShingle | Strang, Gilbert Fast transforms: Banded matrices with banded inverses |
| title | Fast transforms: Banded matrices with banded inverses |
| title_full | Fast transforms: Banded matrices with banded inverses |
| title_fullStr | Fast transforms: Banded matrices with banded inverses |
| title_full_unstemmed | Fast transforms: Banded matrices with banded inverses |
| title_short | Fast transforms: Banded matrices with banded inverses |
| title_sort | fast transforms banded matrices with banded inverses |
| url | http://hdl.handle.net/1721.1/80880 https://orcid.org/0000-0001-7473-9287 |
| work_keys_str_mv | AT stranggilbert fasttransformsbandedmatriceswithbandedinverses |