On relaxed greedy randomized coordinate descent methods for solving large linear least-squares problems

The greedy randomized coordinate descent (GRCD) method is an effective iterative method for solving large linear least-squares problems. In this work, we construct a class of relaxed greedy randomized coordinate descent (RGRCD) methods by introducing a relaxation parameter in the probability criteri...
Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Zhang, Jianhua [verfasserIn] Guo, Jinghui [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2020

Schlagwörter:	Linear least-squares problem Greedy randomized coordinate descent Relaxation

Übergeordnetes Werk:	Enthalten in: Applied numerical mathematics - Amsterdam [u.a.] : Elsevier, 1985, 157, Seite 372-384
Übergeordnetes Werk:	volume:157 ; pages:372-384

DOI / URN:	10.1016/j.apnum.2020.06.014

Katalog-ID:	ELV004492692

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245	1	0	\|a On relaxed greedy randomized coordinate descent methods for solving large linear least-squares problems
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520			\|a The greedy randomized coordinate descent (GRCD) method is an effective iterative method for solving large linear least-squares problems. In this work, we construct a class of relaxed greedy randomized coordinate descent (RGRCD) methods by introducing a relaxation parameter in the probability criterion. Then, we prove the convergence properties of these methods when the coefficient matrix of the linear least-squares problems is of full column rank, with the number of rows being no less than the number of columns. In addition, we propose a max-distance coordinate descent (CD) method, and study its convergence properties and accelerated version. Finally, we provide some numerical experiments to confirm the effectiveness of our new methods.
650		4	\|a Linear least-squares problem
650		4	\|a Greedy randomized coordinate descent
650		4	\|a Relaxation
700	1		\|a Guo, Jinghui \|e verfasserin \|4 aut
773	0	8	\|i Enthalten in \|t Applied numerical mathematics \|d Amsterdam [u.a.] : Elsevier, 1985 \|g 157, Seite 372-384 \|h Online-Ressource \|w (DE-627)266888879 \|w (DE-600)1468770-7 \|w (DE-576)075962314 \|7 nnns
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936	b	k	\|a 31.76 \|j Numerische Mathematik
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allfields	10.1016/j.apnum.2020.06.014 doi (DE-627)ELV004492692 (ELSEVIER)S0168-9274(20)30196-3 DE-627 ger DE-627 rda eng 510 DE-600 31.76 bkl Zhang, Jianhua verfasserin aut On relaxed greedy randomized coordinate descent methods for solving large linear least-squares problems 2020 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier The greedy randomized coordinate descent (GRCD) method is an effective iterative method for solving large linear least-squares problems. In this work, we construct a class of relaxed greedy randomized coordinate descent (RGRCD) methods by introducing a relaxation parameter in the probability criterion. Then, we prove the convergence properties of these methods when the coefficient matrix of the linear least-squares problems is of full column rank, with the number of rows being no less than the number of columns. In addition, we propose a max-distance coordinate descent (CD) method, and study its convergence properties and accelerated version. Finally, we provide some numerical experiments to confirm the effectiveness of our new methods. Linear least-squares problem Greedy randomized coordinate descent Relaxation Guo, Jinghui verfasserin aut Enthalten in Applied numerical mathematics Amsterdam [u.a.] : Elsevier, 1985 157, Seite 372-384 Online-Ressource (DE-627)266888879 (DE-600)1468770-7 (DE-576)075962314 nnns volume:157 pages:372-384 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_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_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4313 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_4393 31.76 Numerische Mathematik AR 157 372-384
spelling	10.1016/j.apnum.2020.06.014 doi (DE-627)ELV004492692 (ELSEVIER)S0168-9274(20)30196-3 DE-627 ger DE-627 rda eng 510 DE-600 31.76 bkl Zhang, Jianhua verfasserin aut On relaxed greedy randomized coordinate descent methods for solving large linear least-squares problems 2020 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier The greedy randomized coordinate descent (GRCD) method is an effective iterative method for solving large linear least-squares problems. In this work, we construct a class of relaxed greedy randomized coordinate descent (RGRCD) methods by introducing a relaxation parameter in the probability criterion. Then, we prove the convergence properties of these methods when the coefficient matrix of the linear least-squares problems is of full column rank, with the number of rows being no less than the number of columns. In addition, we propose a max-distance coordinate descent (CD) method, and study its convergence properties and accelerated version. Finally, we provide some numerical experiments to confirm the effectiveness of our new methods. Linear least-squares problem Greedy randomized coordinate descent Relaxation Guo, Jinghui verfasserin aut Enthalten in Applied numerical mathematics Amsterdam [u.a.] : Elsevier, 1985 157, Seite 372-384 Online-Ressource (DE-627)266888879 (DE-600)1468770-7 (DE-576)075962314 nnns volume:157 pages:372-384 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_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_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4313 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_4393 31.76 Numerische Mathematik AR 157 372-384
allfields_unstemmed	10.1016/j.apnum.2020.06.014 doi (DE-627)ELV004492692 (ELSEVIER)S0168-9274(20)30196-3 DE-627 ger DE-627 rda eng 510 DE-600 31.76 bkl Zhang, Jianhua verfasserin aut On relaxed greedy randomized coordinate descent methods for solving large linear least-squares problems 2020 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier The greedy randomized coordinate descent (GRCD) method is an effective iterative method for solving large linear least-squares problems. In this work, we construct a class of relaxed greedy randomized coordinate descent (RGRCD) methods by introducing a relaxation parameter in the probability criterion. Then, we prove the convergence properties of these methods when the coefficient matrix of the linear least-squares problems is of full column rank, with the number of rows being no less than the number of columns. In addition, we propose a max-distance coordinate descent (CD) method, and study its convergence properties and accelerated version. Finally, we provide some numerical experiments to confirm the effectiveness of our new methods. Linear least-squares problem Greedy randomized coordinate descent Relaxation Guo, Jinghui verfasserin aut Enthalten in Applied numerical mathematics Amsterdam [u.a.] : Elsevier, 1985 157, Seite 372-384 Online-Ressource (DE-627)266888879 (DE-600)1468770-7 (DE-576)075962314 nnns volume:157 pages:372-384 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_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_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4313 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_4393 31.76 Numerische Mathematik AR 157 372-384
allfieldsGer	10.1016/j.apnum.2020.06.014 doi (DE-627)ELV004492692 (ELSEVIER)S0168-9274(20)30196-3 DE-627 ger DE-627 rda eng 510 DE-600 31.76 bkl Zhang, Jianhua verfasserin aut On relaxed greedy randomized coordinate descent methods for solving large linear least-squares problems 2020 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier The greedy randomized coordinate descent (GRCD) method is an effective iterative method for solving large linear least-squares problems. In this work, we construct a class of relaxed greedy randomized coordinate descent (RGRCD) methods by introducing a relaxation parameter in the probability criterion. Then, we prove the convergence properties of these methods when the coefficient matrix of the linear least-squares problems is of full column rank, with the number of rows being no less than the number of columns. In addition, we propose a max-distance coordinate descent (CD) method, and study its convergence properties and accelerated version. Finally, we provide some numerical experiments to confirm the effectiveness of our new methods. Linear least-squares problem Greedy randomized coordinate descent Relaxation Guo, Jinghui verfasserin aut Enthalten in Applied numerical mathematics Amsterdam [u.a.] : Elsevier, 1985 157, Seite 372-384 Online-Ressource (DE-627)266888879 (DE-600)1468770-7 (DE-576)075962314 nnns volume:157 pages:372-384 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_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_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4313 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_4393 31.76 Numerische Mathematik AR 157 372-384
allfieldsSound	10.1016/j.apnum.2020.06.014 doi (DE-627)ELV004492692 (ELSEVIER)S0168-9274(20)30196-3 DE-627 ger DE-627 rda eng 510 DE-600 31.76 bkl Zhang, Jianhua verfasserin aut On relaxed greedy randomized coordinate descent methods for solving large linear least-squares problems 2020 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier The greedy randomized coordinate descent (GRCD) method is an effective iterative method for solving large linear least-squares problems. In this work, we construct a class of relaxed greedy randomized coordinate descent (RGRCD) methods by introducing a relaxation parameter in the probability criterion. Then, we prove the convergence properties of these methods when the coefficient matrix of the linear least-squares problems is of full column rank, with the number of rows being no less than the number of columns. In addition, we propose a max-distance coordinate descent (CD) method, and study its convergence properties and accelerated version. Finally, we provide some numerical experiments to confirm the effectiveness of our new methods. Linear least-squares problem Greedy randomized coordinate descent Relaxation Guo, Jinghui verfasserin aut Enthalten in Applied numerical mathematics Amsterdam [u.a.] : Elsevier, 1985 157, Seite 372-384 Online-Ressource (DE-627)266888879 (DE-600)1468770-7 (DE-576)075962314 nnns volume:157 pages:372-384 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_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_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4313 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_4393 31.76 Numerische Mathematik AR 157 372-384
language	English
source	Enthalten in Applied numerical mathematics 157, Seite 372-384 volume:157 pages:372-384
sourceStr	Enthalten in Applied numerical mathematics 157, Seite 372-384 volume:157 pages:372-384
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topic_facet	Linear least-squares problem Greedy randomized coordinate descent Relaxation
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authorswithroles_txt_mv	Zhang, Jianhua @@aut@@ Guo, Jinghui @@aut@@
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author	Zhang, Jianhua
spellingShingle	Zhang, Jianhua ddc 510 bkl 31.76 misc Linear least-squares problem misc Greedy randomized coordinate descent misc Relaxation On relaxed greedy randomized coordinate descent methods for solving large linear least-squares problems
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topic_title	510 DE-600 31.76 bkl On relaxed greedy randomized coordinate descent methods for solving large linear least-squares problems Linear least-squares problem Greedy randomized coordinate descent Relaxation
topic	ddc 510 bkl 31.76 misc Linear least-squares problem misc Greedy randomized coordinate descent misc Relaxation
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title	On relaxed greedy randomized coordinate descent methods for solving large linear least-squares problems
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title_full	On relaxed greedy randomized coordinate descent methods for solving large linear least-squares problems
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title_sort	on relaxed greedy randomized coordinate descent methods for solving large linear least-squares problems
title_auth	On relaxed greedy randomized coordinate descent methods for solving large linear least-squares problems
abstract	The greedy randomized coordinate descent (GRCD) method is an effective iterative method for solving large linear least-squares problems. In this work, we construct a class of relaxed greedy randomized coordinate descent (RGRCD) methods by introducing a relaxation parameter in the probability criterion. Then, we prove the convergence properties of these methods when the coefficient matrix of the linear least-squares problems is of full column rank, with the number of rows being no less than the number of columns. In addition, we propose a max-distance coordinate descent (CD) method, and study its convergence properties and accelerated version. Finally, we provide some numerical experiments to confirm the effectiveness of our new methods.
abstractGer	The greedy randomized coordinate descent (GRCD) method is an effective iterative method for solving large linear least-squares problems. In this work, we construct a class of relaxed greedy randomized coordinate descent (RGRCD) methods by introducing a relaxation parameter in the probability criterion. Then, we prove the convergence properties of these methods when the coefficient matrix of the linear least-squares problems is of full column rank, with the number of rows being no less than the number of columns. In addition, we propose a max-distance coordinate descent (CD) method, and study its convergence properties and accelerated version. Finally, we provide some numerical experiments to confirm the effectiveness of our new methods.
abstract_unstemmed	The greedy randomized coordinate descent (GRCD) method is an effective iterative method for solving large linear least-squares problems. In this work, we construct a class of relaxed greedy randomized coordinate descent (RGRCD) methods by introducing a relaxation parameter in the probability criterion. Then, we prove the convergence properties of these methods when the coefficient matrix of the linear least-squares problems is of full column rank, with the number of rows being no less than the number of columns. In addition, we propose a max-distance coordinate descent (CD) method, and study its convergence properties and accelerated version. Finally, we provide some numerical experiments to confirm the effectiveness of our new methods.
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title_short	On relaxed greedy randomized coordinate descent methods for solving large linear least-squares problems
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doi_str	10.1016/j.apnum.2020.06.014
up_date	2024-07-06T23:10:32.438Z
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On relaxed greedy randomized coordinate descent methods for solving large linear least-squares problems

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