Inversion of Displacement Operators: Inversion of displacement operators
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| Title: | Inversion of Displacement Operators: Inversion of displacement operators |
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| Authors: | Victor Y. Pan, Xinmao Wang |
| Source: | SIAM Journal on Matrix Analysis and Applications. 24:660-677 |
| Publisher Information: | Society for Industrial & Applied Mathematics (SIAM), 2003. |
| Publication Year: | 2003 |
| Subject Terms: | tangential confluent Nevanlinna-Pick problem, Applications of operator theory in numerical analysis, Analysis of algorithms and problem complexity, displacement rank, Toeplitz operators, Hankel operators, Wiener-Hopf operators, structured matrices, 0102 computer and information sciences, 0101 mathematics, Direct numerical methods for linear systems and matrix inversion, Linear operator methods in interpolation, moment and extension problems, 01 natural sciences, inverse displacement operators |
| Description: | It is known that an \(n\times n\) structured matrix \(M\) can be associated with an appropriate displacement operator \(L\) such that the rank \(r\) of \(L(M)\) satisfies \(r\ll n\) and the \(n^2\) entries of \(L(M)\) can be represented via only \(2rn\) parameters. The authors present a general method to express \(M\) via \(L(M)\) under very mild nonsingularity assumptions. The method unifies the derivation of known formulae and gives new formulae, in particular for the tangential Nevalinna-Pick problems. It accelerates known solution algorithms. The authors obtain general new matrix representations in the confluent case and substantially improve the known estimates for the norm \(\| L^{-1}\| \) which is critical in computations based on the displacement approach. |
| Document Type: | Article |
| File Description: | application/xml |
| Language: | English |
| ISSN: | 1095-7162 0895-4798 |
| DOI: | 10.1137/s089547980238627x |
| Access URL: | https://zbmath.org/2027918 https://doi.org/10.1137/s089547980238627x https://epubs.siam.org/doi/abs/10.1137/S089547980238627X https://dl.acm.org/doi/10.1137/S089547980238627X http://comet.lehman.cuny.edu/vpan/pdf/pan195.pdf https://dblp.uni-trier.de/db/journals/siammax/siammax24.html#PanW03 |
| Accession Number: | edsair.doi.dedup.....dbbea08b9b7ba1cc4b9c16c0e9a8e1fc |
| Database: | OpenAIRE |
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Nájsť tento článok vo Web of Science | Abstract: | It is known that an \(n\times n\) structured matrix \(M\) can be associated with an appropriate displacement operator \(L\) such that the rank \(r\) of \(L(M)\) satisfies \(r\ll n\) and the \(n^2\) entries of \(L(M)\) can be represented via only \(2rn\) parameters. The authors present a general method to express \(M\) via \(L(M)\) under very mild nonsingularity assumptions. The method unifies the derivation of known formulae and gives new formulae, in particular for the tangential Nevalinna-Pick problems. It accelerates known solution algorithms. The authors obtain general new matrix representations in the confluent case and substantially improve the known estimates for the norm \(\| L^{-1}\| \) which is critical in computations based on the displacement approach. |
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| ISSN: | 10957162 08954798 |
| DOI: | 10.1137/s089547980238627x |