The least-squares method for matrices dependent on parameters
Abstract Some algorithms are suggested for constructing pseudoinverse matrices and for solving systems with rectangular matrices whose entries depend on a parameter in polynomial and rational ways. The cases of one- and two-parameter matrices are considered. The construction of pseudoinverse matrice...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Kublanovskaya, V. N. [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
1997 |
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| Schlagwörter: |
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| Anmerkung: |
© Plenum Publishing Corporation 1997 |
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| Übergeordnetes Werk: |
Enthalten in: Journal of mathematical sciences - Kluwer Academic Publishers-Plenum Publishers, 1994, 86(1997), 4 vom: Sept., Seite 2920-2925 |
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volume:86 ; year:1997 ; number:4 ; month:09 ; pages:2920-2925 |
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| DOI / URN: |
10.1007/BF02356147 |
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| 520 | |a Abstract Some algorithms are suggested for constructing pseudoinverse matrices and for solving systems with rectangular matrices whose entries depend on a parameter in polynomial and rational ways. The cases of one- and two-parameter matrices are considered. The construction of pseudoinverse matrices are realized on the basis of rank factorization algorithms. In the case of matrices with polynomial occurrence of parameters, these algorithms are the ΔW-1 and ΔW-2 algorithms for one- and two-parameter matrices, respectively. In the case of matrices with rational occurrence of parameters, these algorithms are the irreducible factorization algorithms. This paper is a continuation of the author's studies of the solution of systems with one-parameter matrices and an extension of the results to the case of two-parameter matrices with polynomial and rational entries. Bibliography: 12 titles. | ||
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10.1007/BF02356147 doi (DE-627)OLC2030748218 (DE-He213)BF02356147-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn 31.00 bkl Kublanovskaya, V. N. verfasserin aut The least-squares method for matrices dependent on parameters 1997 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Plenum Publishing Corporation 1997 Abstract Some algorithms are suggested for constructing pseudoinverse matrices and for solving systems with rectangular matrices whose entries depend on a parameter in polynomial and rational ways. The cases of one- and two-parameter matrices are considered. The construction of pseudoinverse matrices are realized on the basis of rank factorization algorithms. In the case of matrices with polynomial occurrence of parameters, these algorithms are the ΔW-1 and ΔW-2 algorithms for one- and two-parameter matrices, respectively. In the case of matrices with rational occurrence of parameters, these algorithms are the irreducible factorization algorithms. This paper is a continuation of the author's studies of the solution of systems with one-parameter matrices and an extension of the results to the case of two-parameter matrices with polynomial and rational entries. Bibliography: 12 titles. Rational Occurrence Rational Entry Irreducible Factorization Factorization Algorithm Rank Factorization Enthalten in Journal of mathematical sciences Kluwer Academic Publishers-Plenum Publishers, 1994 86(1997), 4 vom: Sept., Seite 2920-2925 (DE-627)18219762X (DE-600)1185490-X (DE-576)038888130 1072-3374 nnns volume:86 year:1997 number:4 month:09 pages:2920-2925 https://doi.org/10.1007/BF02356147 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_22 GBV_ILN_40 GBV_ILN_70 GBV_ILN_2005 GBV_ILN_2088 GBV_ILN_2409 GBV_ILN_4012 GBV_ILN_4310 GBV_ILN_4314 GBV_ILN_4325 31.00 VZ AR 86 1997 4 09 2920-2925 |
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10.1007/BF02356147 doi (DE-627)OLC2030748218 (DE-He213)BF02356147-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn 31.00 bkl Kublanovskaya, V. N. verfasserin aut The least-squares method for matrices dependent on parameters 1997 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Plenum Publishing Corporation 1997 Abstract Some algorithms are suggested for constructing pseudoinverse matrices and for solving systems with rectangular matrices whose entries depend on a parameter in polynomial and rational ways. The cases of one- and two-parameter matrices are considered. The construction of pseudoinverse matrices are realized on the basis of rank factorization algorithms. In the case of matrices with polynomial occurrence of parameters, these algorithms are the ΔW-1 and ΔW-2 algorithms for one- and two-parameter matrices, respectively. In the case of matrices with rational occurrence of parameters, these algorithms are the irreducible factorization algorithms. This paper is a continuation of the author's studies of the solution of systems with one-parameter matrices and an extension of the results to the case of two-parameter matrices with polynomial and rational entries. Bibliography: 12 titles. Rational Occurrence Rational Entry Irreducible Factorization Factorization Algorithm Rank Factorization Enthalten in Journal of mathematical sciences Kluwer Academic Publishers-Plenum Publishers, 1994 86(1997), 4 vom: Sept., Seite 2920-2925 (DE-627)18219762X (DE-600)1185490-X (DE-576)038888130 1072-3374 nnns volume:86 year:1997 number:4 month:09 pages:2920-2925 https://doi.org/10.1007/BF02356147 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_22 GBV_ILN_40 GBV_ILN_70 GBV_ILN_2005 GBV_ILN_2088 GBV_ILN_2409 GBV_ILN_4012 GBV_ILN_4310 GBV_ILN_4314 GBV_ILN_4325 31.00 VZ AR 86 1997 4 09 2920-2925 |
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10.1007/BF02356147 doi (DE-627)OLC2030748218 (DE-He213)BF02356147-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn 31.00 bkl Kublanovskaya, V. N. verfasserin aut The least-squares method for matrices dependent on parameters 1997 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Plenum Publishing Corporation 1997 Abstract Some algorithms are suggested for constructing pseudoinverse matrices and for solving systems with rectangular matrices whose entries depend on a parameter in polynomial and rational ways. The cases of one- and two-parameter matrices are considered. The construction of pseudoinverse matrices are realized on the basis of rank factorization algorithms. In the case of matrices with polynomial occurrence of parameters, these algorithms are the ΔW-1 and ΔW-2 algorithms for one- and two-parameter matrices, respectively. In the case of matrices with rational occurrence of parameters, these algorithms are the irreducible factorization algorithms. This paper is a continuation of the author's studies of the solution of systems with one-parameter matrices and an extension of the results to the case of two-parameter matrices with polynomial and rational entries. Bibliography: 12 titles. Rational Occurrence Rational Entry Irreducible Factorization Factorization Algorithm Rank Factorization Enthalten in Journal of mathematical sciences Kluwer Academic Publishers-Plenum Publishers, 1994 86(1997), 4 vom: Sept., Seite 2920-2925 (DE-627)18219762X (DE-600)1185490-X (DE-576)038888130 1072-3374 nnns volume:86 year:1997 number:4 month:09 pages:2920-2925 https://doi.org/10.1007/BF02356147 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_22 GBV_ILN_40 GBV_ILN_70 GBV_ILN_2005 GBV_ILN_2088 GBV_ILN_2409 GBV_ILN_4012 GBV_ILN_4310 GBV_ILN_4314 GBV_ILN_4325 31.00 VZ AR 86 1997 4 09 2920-2925 |
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10.1007/BF02356147 doi (DE-627)OLC2030748218 (DE-He213)BF02356147-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn 31.00 bkl Kublanovskaya, V. N. verfasserin aut The least-squares method for matrices dependent on parameters 1997 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Plenum Publishing Corporation 1997 Abstract Some algorithms are suggested for constructing pseudoinverse matrices and for solving systems with rectangular matrices whose entries depend on a parameter in polynomial and rational ways. The cases of one- and two-parameter matrices are considered. The construction of pseudoinverse matrices are realized on the basis of rank factorization algorithms. In the case of matrices with polynomial occurrence of parameters, these algorithms are the ΔW-1 and ΔW-2 algorithms for one- and two-parameter matrices, respectively. In the case of matrices with rational occurrence of parameters, these algorithms are the irreducible factorization algorithms. This paper is a continuation of the author's studies of the solution of systems with one-parameter matrices and an extension of the results to the case of two-parameter matrices with polynomial and rational entries. Bibliography: 12 titles. Rational Occurrence Rational Entry Irreducible Factorization Factorization Algorithm Rank Factorization Enthalten in Journal of mathematical sciences Kluwer Academic Publishers-Plenum Publishers, 1994 86(1997), 4 vom: Sept., Seite 2920-2925 (DE-627)18219762X (DE-600)1185490-X (DE-576)038888130 1072-3374 nnns volume:86 year:1997 number:4 month:09 pages:2920-2925 https://doi.org/10.1007/BF02356147 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_22 GBV_ILN_40 GBV_ILN_70 GBV_ILN_2005 GBV_ILN_2088 GBV_ILN_2409 GBV_ILN_4012 GBV_ILN_4310 GBV_ILN_4314 GBV_ILN_4325 31.00 VZ AR 86 1997 4 09 2920-2925 |
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10.1007/BF02356147 doi (DE-627)OLC2030748218 (DE-He213)BF02356147-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn 31.00 bkl Kublanovskaya, V. N. verfasserin aut The least-squares method for matrices dependent on parameters 1997 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Plenum Publishing Corporation 1997 Abstract Some algorithms are suggested for constructing pseudoinverse matrices and for solving systems with rectangular matrices whose entries depend on a parameter in polynomial and rational ways. The cases of one- and two-parameter matrices are considered. The construction of pseudoinverse matrices are realized on the basis of rank factorization algorithms. In the case of matrices with polynomial occurrence of parameters, these algorithms are the ΔW-1 and ΔW-2 algorithms for one- and two-parameter matrices, respectively. In the case of matrices with rational occurrence of parameters, these algorithms are the irreducible factorization algorithms. This paper is a continuation of the author's studies of the solution of systems with one-parameter matrices and an extension of the results to the case of two-parameter matrices with polynomial and rational entries. Bibliography: 12 titles. Rational Occurrence Rational Entry Irreducible Factorization Factorization Algorithm Rank Factorization Enthalten in Journal of mathematical sciences Kluwer Academic Publishers-Plenum Publishers, 1994 86(1997), 4 vom: Sept., Seite 2920-2925 (DE-627)18219762X (DE-600)1185490-X (DE-576)038888130 1072-3374 nnns volume:86 year:1997 number:4 month:09 pages:2920-2925 https://doi.org/10.1007/BF02356147 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_22 GBV_ILN_40 GBV_ILN_70 GBV_ILN_2005 GBV_ILN_2088 GBV_ILN_2409 GBV_ILN_4012 GBV_ILN_4310 GBV_ILN_4314 GBV_ILN_4325 31.00 VZ AR 86 1997 4 09 2920-2925 |
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Abstract Some algorithms are suggested for constructing pseudoinverse matrices and for solving systems with rectangular matrices whose entries depend on a parameter in polynomial and rational ways. The cases of one- and two-parameter matrices are considered. The construction of pseudoinverse matrices are realized on the basis of rank factorization algorithms. In the case of matrices with polynomial occurrence of parameters, these algorithms are the ΔW-1 and ΔW-2 algorithms for one- and two-parameter matrices, respectively. In the case of matrices with rational occurrence of parameters, these algorithms are the irreducible factorization algorithms. This paper is a continuation of the author's studies of the solution of systems with one-parameter matrices and an extension of the results to the case of two-parameter matrices with polynomial and rational entries. Bibliography: 12 titles. © Plenum Publishing Corporation 1997 |
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Abstract Some algorithms are suggested for constructing pseudoinverse matrices and for solving systems with rectangular matrices whose entries depend on a parameter in polynomial and rational ways. The cases of one- and two-parameter matrices are considered. The construction of pseudoinverse matrices are realized on the basis of rank factorization algorithms. In the case of matrices with polynomial occurrence of parameters, these algorithms are the ΔW-1 and ΔW-2 algorithms for one- and two-parameter matrices, respectively. In the case of matrices with rational occurrence of parameters, these algorithms are the irreducible factorization algorithms. This paper is a continuation of the author's studies of the solution of systems with one-parameter matrices and an extension of the results to the case of two-parameter matrices with polynomial and rational entries. Bibliography: 12 titles. © Plenum Publishing Corporation 1997 |
| abstract_unstemmed |
Abstract Some algorithms are suggested for constructing pseudoinverse matrices and for solving systems with rectangular matrices whose entries depend on a parameter in polynomial and rational ways. The cases of one- and two-parameter matrices are considered. The construction of pseudoinverse matrices are realized on the basis of rank factorization algorithms. In the case of matrices with polynomial occurrence of parameters, these algorithms are the ΔW-1 and ΔW-2 algorithms for one- and two-parameter matrices, respectively. In the case of matrices with rational occurrence of parameters, these algorithms are the irreducible factorization algorithms. This paper is a continuation of the author's studies of the solution of systems with one-parameter matrices and an extension of the results to the case of two-parameter matrices with polynomial and rational entries. Bibliography: 12 titles. © Plenum Publishing Corporation 1997 |
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The least-squares method for matrices dependent on parameters |
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