An inverse eigenvalue problem for doubly periodic pseudo-Jacobi matrices

In this paper, we investigate a direct and an inverse eigenvalue problem to recover doubly periodic pseudo-Jacobi matrices from three spectra λ , μ...
Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Xu, Wei-Ru [verfasserIn] Bebiano, Natália [verfasserIn] Chen, Guo-Liang [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2021

Schlagwörter:	Inverse eigenvalue problem Doubly periodic tridiagonal matrix Pseudo-Jacobi matrix Periodic pseudo-Jacobi matrix Spectrum

Übergeordnetes Werk:	Enthalten in: Journal of computational and applied mathematics - Amsterdam [u.a.] : North-Holland, 1975, 405
Übergeordnetes Werk:	volume:405

DOI / URN:	10.1016/j.cam.2021.113957

Katalog-ID:	ELV007188560

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245	1	0	\|a An inverse eigenvalue problem for doubly periodic pseudo-Jacobi matrices
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520			\|a In this paper, we investigate a direct and an inverse eigenvalue problem to recover doubly periodic pseudo-Jacobi matrices from three spectra λ , μ 1 , μ 2 and two positive numbers β ⋆ , β ♢ . Necessary and sufficient conditions for the existence of solution are given and numerical algorithms, using a modified unsymmetric Lanczos scheme, to reconstruct the matrix from the prescribed data are proposed. Some illustrative numerical examples are presented. The obtained results recover and extend several existing results in the literature.
650		4	\|a Inverse eigenvalue problem
650		4	\|a Doubly periodic tridiagonal matrix
650		4	\|a Pseudo-Jacobi matrix
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allfields	10.1016/j.cam.2021.113957 doi (DE-627)ELV007188560 (ELSEVIER)S0377-0427(21)00564-1 DE-627 ger DE-627 rda eng 510 DE-600 31.00 bkl Xu, Wei-Ru verfasserin aut An inverse eigenvalue problem for doubly periodic pseudo-Jacobi matrices 2021 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In this paper, we investigate a direct and an inverse eigenvalue problem to recover doubly periodic pseudo-Jacobi matrices from three spectra λ , μ 1 , μ 2 and two positive numbers β ⋆ , β ♢ . Necessary and sufficient conditions for the existence of solution are given and numerical algorithms, using a modified unsymmetric Lanczos scheme, to reconstruct the matrix from the prescribed data are proposed. Some illustrative numerical examples are presented. The obtained results recover and extend several existing results in the literature. Inverse eigenvalue problem Doubly periodic tridiagonal matrix Pseudo-Jacobi matrix Periodic pseudo-Jacobi matrix Spectrum Bebiano, Natália verfasserin (orcid)0000-0003-2600-6489 aut Chen, Guo-Liang verfasserin aut Enthalten in Journal of computational and applied mathematics Amsterdam [u.a.] : North-Holland, 1975 405 Online-Ressource (DE-627)266889204 (DE-600)1468806-2 (DE-576)075962373 nnns volume:405 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_224 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4392 GBV_ILN_4393 GBV_ILN_4700 31.00 Mathematik: Allgemeines AR 405
spelling	10.1016/j.cam.2021.113957 doi (DE-627)ELV007188560 (ELSEVIER)S0377-0427(21)00564-1 DE-627 ger DE-627 rda eng 510 DE-600 31.00 bkl Xu, Wei-Ru verfasserin aut An inverse eigenvalue problem for doubly periodic pseudo-Jacobi matrices 2021 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In this paper, we investigate a direct and an inverse eigenvalue problem to recover doubly periodic pseudo-Jacobi matrices from three spectra λ , μ 1 , μ 2 and two positive numbers β ⋆ , β ♢ . Necessary and sufficient conditions for the existence of solution are given and numerical algorithms, using a modified unsymmetric Lanczos scheme, to reconstruct the matrix from the prescribed data are proposed. Some illustrative numerical examples are presented. The obtained results recover and extend several existing results in the literature. Inverse eigenvalue problem Doubly periodic tridiagonal matrix Pseudo-Jacobi matrix Periodic pseudo-Jacobi matrix Spectrum Bebiano, Natália verfasserin (orcid)0000-0003-2600-6489 aut Chen, Guo-Liang verfasserin aut Enthalten in Journal of computational and applied mathematics Amsterdam [u.a.] : North-Holland, 1975 405 Online-Ressource (DE-627)266889204 (DE-600)1468806-2 (DE-576)075962373 nnns volume:405 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_224 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4392 GBV_ILN_4393 GBV_ILN_4700 31.00 Mathematik: Allgemeines AR 405
allfields_unstemmed	10.1016/j.cam.2021.113957 doi (DE-627)ELV007188560 (ELSEVIER)S0377-0427(21)00564-1 DE-627 ger DE-627 rda eng 510 DE-600 31.00 bkl Xu, Wei-Ru verfasserin aut An inverse eigenvalue problem for doubly periodic pseudo-Jacobi matrices 2021 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In this paper, we investigate a direct and an inverse eigenvalue problem to recover doubly periodic pseudo-Jacobi matrices from three spectra λ , μ 1 , μ 2 and two positive numbers β ⋆ , β ♢ . Necessary and sufficient conditions for the existence of solution are given and numerical algorithms, using a modified unsymmetric Lanczos scheme, to reconstruct the matrix from the prescribed data are proposed. Some illustrative numerical examples are presented. The obtained results recover and extend several existing results in the literature. Inverse eigenvalue problem Doubly periodic tridiagonal matrix Pseudo-Jacobi matrix Periodic pseudo-Jacobi matrix Spectrum Bebiano, Natália verfasserin (orcid)0000-0003-2600-6489 aut Chen, Guo-Liang verfasserin aut Enthalten in Journal of computational and applied mathematics Amsterdam [u.a.] : North-Holland, 1975 405 Online-Ressource (DE-627)266889204 (DE-600)1468806-2 (DE-576)075962373 nnns volume:405 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_224 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4392 GBV_ILN_4393 GBV_ILN_4700 31.00 Mathematik: Allgemeines AR 405
allfieldsGer	10.1016/j.cam.2021.113957 doi (DE-627)ELV007188560 (ELSEVIER)S0377-0427(21)00564-1 DE-627 ger DE-627 rda eng 510 DE-600 31.00 bkl Xu, Wei-Ru verfasserin aut An inverse eigenvalue problem for doubly periodic pseudo-Jacobi matrices 2021 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In this paper, we investigate a direct and an inverse eigenvalue problem to recover doubly periodic pseudo-Jacobi matrices from three spectra λ , μ 1 , μ 2 and two positive numbers β ⋆ , β ♢ . Necessary and sufficient conditions for the existence of solution are given and numerical algorithms, using a modified unsymmetric Lanczos scheme, to reconstruct the matrix from the prescribed data are proposed. Some illustrative numerical examples are presented. The obtained results recover and extend several existing results in the literature. Inverse eigenvalue problem Doubly periodic tridiagonal matrix Pseudo-Jacobi matrix Periodic pseudo-Jacobi matrix Spectrum Bebiano, Natália verfasserin (orcid)0000-0003-2600-6489 aut Chen, Guo-Liang verfasserin aut Enthalten in Journal of computational and applied mathematics Amsterdam [u.a.] : North-Holland, 1975 405 Online-Ressource (DE-627)266889204 (DE-600)1468806-2 (DE-576)075962373 nnns volume:405 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_224 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4392 GBV_ILN_4393 GBV_ILN_4700 31.00 Mathematik: Allgemeines AR 405
allfieldsSound	10.1016/j.cam.2021.113957 doi (DE-627)ELV007188560 (ELSEVIER)S0377-0427(21)00564-1 DE-627 ger DE-627 rda eng 510 DE-600 31.00 bkl Xu, Wei-Ru verfasserin aut An inverse eigenvalue problem for doubly periodic pseudo-Jacobi matrices 2021 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In this paper, we investigate a direct and an inverse eigenvalue problem to recover doubly periodic pseudo-Jacobi matrices from three spectra λ , μ 1 , μ 2 and two positive numbers β ⋆ , β ♢ . Necessary and sufficient conditions for the existence of solution are given and numerical algorithms, using a modified unsymmetric Lanczos scheme, to reconstruct the matrix from the prescribed data are proposed. Some illustrative numerical examples are presented. The obtained results recover and extend several existing results in the literature. Inverse eigenvalue problem Doubly periodic tridiagonal matrix Pseudo-Jacobi matrix Periodic pseudo-Jacobi matrix Spectrum Bebiano, Natália verfasserin (orcid)0000-0003-2600-6489 aut Chen, Guo-Liang verfasserin aut Enthalten in Journal of computational and applied mathematics Amsterdam [u.a.] : North-Holland, 1975 405 Online-Ressource (DE-627)266889204 (DE-600)1468806-2 (DE-576)075962373 nnns volume:405 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_224 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4392 GBV_ILN_4393 GBV_ILN_4700 31.00 Mathematik: Allgemeines AR 405
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author	Xu, Wei-Ru
spellingShingle	Xu, Wei-Ru ddc 510 bkl 31.00 misc Inverse eigenvalue problem misc Doubly periodic tridiagonal matrix misc Pseudo-Jacobi matrix misc Periodic pseudo-Jacobi matrix misc Spectrum An inverse eigenvalue problem for doubly periodic pseudo-Jacobi matrices
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topic_title	510 DE-600 31.00 bkl An inverse eigenvalue problem for doubly periodic pseudo-Jacobi matrices Inverse eigenvalue problem Doubly periodic tridiagonal matrix Pseudo-Jacobi matrix Periodic pseudo-Jacobi matrix Spectrum
topic	ddc 510 bkl 31.00 misc Inverse eigenvalue problem misc Doubly periodic tridiagonal matrix misc Pseudo-Jacobi matrix misc Periodic pseudo-Jacobi matrix misc Spectrum
topic_unstemmed	ddc 510 bkl 31.00 misc Inverse eigenvalue problem misc Doubly periodic tridiagonal matrix misc Pseudo-Jacobi matrix misc Periodic pseudo-Jacobi matrix misc Spectrum
topic_browse	ddc 510 bkl 31.00 misc Inverse eigenvalue problem misc Doubly periodic tridiagonal matrix misc Pseudo-Jacobi matrix misc Periodic pseudo-Jacobi matrix misc Spectrum
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title	An inverse eigenvalue problem for doubly periodic pseudo-Jacobi matrices
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title_full	An inverse eigenvalue problem for doubly periodic pseudo-Jacobi matrices
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author_browse	Xu, Wei-Ru Bebiano, Natália Chen, Guo-Liang
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title_sort	an inverse eigenvalue problem for doubly periodic pseudo-jacobi matrices
title_auth	An inverse eigenvalue problem for doubly periodic pseudo-Jacobi matrices
abstract	In this paper, we investigate a direct and an inverse eigenvalue problem to recover doubly periodic pseudo-Jacobi matrices from three spectra λ , μ 1 , μ 2 and two positive numbers β ⋆ , β ♢ . Necessary and sufficient conditions for the existence of solution are given and numerical algorithms, using a modified unsymmetric Lanczos scheme, to reconstruct the matrix from the prescribed data are proposed. Some illustrative numerical examples are presented. The obtained results recover and extend several existing results in the literature.
abstractGer	In this paper, we investigate a direct and an inverse eigenvalue problem to recover doubly periodic pseudo-Jacobi matrices from three spectra λ , μ 1 , μ 2 and two positive numbers β ⋆ , β ♢ . Necessary and sufficient conditions for the existence of solution are given and numerical algorithms, using a modified unsymmetric Lanczos scheme, to reconstruct the matrix from the prescribed data are proposed. Some illustrative numerical examples are presented. The obtained results recover and extend several existing results in the literature.
abstract_unstemmed	In this paper, we investigate a direct and an inverse eigenvalue problem to recover doubly periodic pseudo-Jacobi matrices from three spectra λ , μ 1 , μ 2 and two positive numbers β ⋆ , β ♢ . Necessary and sufficient conditions for the existence of solution are given and numerical algorithms, using a modified unsymmetric Lanczos scheme, to reconstruct the matrix from the prescribed data are proposed. Some illustrative numerical examples are presented. The obtained results recover and extend several existing results in the literature.
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title_short	An inverse eigenvalue problem for doubly periodic pseudo-Jacobi matrices
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author2	Bebiano, Natália Chen, Guo-Liang
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doi_str	10.1016/j.cam.2021.113957
up_date	2024-07-06T23:54:34.838Z
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Necessary and sufficient conditions for the existence of solution are given and numerical algorithms, using a modified unsymmetric Lanczos scheme, to reconstruct the matrix from the prescribed data are proposed. Some illustrative numerical examples are presented. 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An inverse eigenvalue problem for doubly periodic pseudo-Jacobi matrices

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