Convergence analysis of modified Newton-HSS method for solving systems of nonlinear equations
Abstract Hermitian and skew-Hermitian splitting(HSS) method has been proved quite successfully in solving large sparse non-Hermitian positive definite systems of linear equations. Recently, by making use of HSS method as inner iteration, Newton-HSS method for solving the systems of nonlinear equatio...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Wu, Qingbiao [verfasserIn] |
|---|
| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2013 |
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| Schlagwörter: |
Hermitian and Skew-Hermitian splitting |
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| Anmerkung: |
© Springer Science+Business Media New York 2013 |
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| Übergeordnetes Werk: |
Enthalten in: Numerical algorithms - Springer US, 1991, 64(2013), 4 vom: 18. Jan., Seite 659-683 |
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| Übergeordnetes Werk: |
volume:64 ; year:2013 ; number:4 ; day:18 ; month:01 ; pages:659-683 |
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| DOI / URN: |
10.1007/s11075-012-9684-5 |
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OLC2051162425 |
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| 520 | |a Abstract Hermitian and skew-Hermitian splitting(HSS) method has been proved quite successfully in solving large sparse non-Hermitian positive definite systems of linear equations. Recently, by making use of HSS method as inner iteration, Newton-HSS method for solving the systems of nonlinear equations with non-Hermitian positive definite Jacobian matrices has been proposed by Bai and Guo. It has shown that the Newton-HSS method outperforms the Newton-USOR and the Newton-GMRES iteration methods. In this paper, a class of modified Newton-HSS methods for solving large systems of nonlinear equations is discussed. In our method, the modified Newton method with R-order of convergence three at least is used to solve the nonlinear equations, and the HSS method is applied to approximately solve the Newton equations. For this class of inexact Newton methods, local and semilocal convergence theorems are proved under suitable conditions. Moreover, a globally convergent modified Newton-HSS method is introduced and a basic global convergence theorem is proved. Numerical results are given to confirm the effectiveness of our method. | ||
| 650 | 4 | |a Hermitian and Skew-Hermitian splitting | |
| 650 | 4 | |a Newton-HSS method | |
| 650 | 4 | |a Large sparse systems | |
| 650 | 4 | |a Nonlinear equations | |
| 650 | 4 | |a Positive-definite Jacobian matrices | |
| 650 | 4 | |a Convergence analysis | |
| 700 | 1 | |a Chen, Minhong |4 aut | |
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10.1007/s11075-012-9684-5 doi (DE-627)OLC2051162425 (DE-He213)s11075-012-9684-5-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Wu, Qingbiao verfasserin aut Convergence analysis of modified Newton-HSS method for solving systems of nonlinear equations 2013 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media New York 2013 Abstract Hermitian and skew-Hermitian splitting(HSS) method has been proved quite successfully in solving large sparse non-Hermitian positive definite systems of linear equations. Recently, by making use of HSS method as inner iteration, Newton-HSS method for solving the systems of nonlinear equations with non-Hermitian positive definite Jacobian matrices has been proposed by Bai and Guo. It has shown that the Newton-HSS method outperforms the Newton-USOR and the Newton-GMRES iteration methods. In this paper, a class of modified Newton-HSS methods for solving large systems of nonlinear equations is discussed. In our method, the modified Newton method with R-order of convergence three at least is used to solve the nonlinear equations, and the HSS method is applied to approximately solve the Newton equations. For this class of inexact Newton methods, local and semilocal convergence theorems are proved under suitable conditions. Moreover, a globally convergent modified Newton-HSS method is introduced and a basic global convergence theorem is proved. Numerical results are given to confirm the effectiveness of our method. Hermitian and Skew-Hermitian splitting Newton-HSS method Large sparse systems Nonlinear equations Positive-definite Jacobian matrices Convergence analysis Chen, Minhong aut Enthalten in Numerical algorithms Springer US, 1991 64(2013), 4 vom: 18. Jan., Seite 659-683 (DE-627)130981753 (DE-600)1075844-6 (DE-576)029154111 1017-1398 nnns volume:64 year:2013 number:4 day:18 month:01 pages:659-683 https://doi.org/10.1007/s11075-012-9684-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 GBV_ILN_2088 AR 64 2013 4 18 01 659-683 |
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10.1007/s11075-012-9684-5 doi (DE-627)OLC2051162425 (DE-He213)s11075-012-9684-5-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Wu, Qingbiao verfasserin aut Convergence analysis of modified Newton-HSS method for solving systems of nonlinear equations 2013 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media New York 2013 Abstract Hermitian and skew-Hermitian splitting(HSS) method has been proved quite successfully in solving large sparse non-Hermitian positive definite systems of linear equations. Recently, by making use of HSS method as inner iteration, Newton-HSS method for solving the systems of nonlinear equations with non-Hermitian positive definite Jacobian matrices has been proposed by Bai and Guo. It has shown that the Newton-HSS method outperforms the Newton-USOR and the Newton-GMRES iteration methods. In this paper, a class of modified Newton-HSS methods for solving large systems of nonlinear equations is discussed. In our method, the modified Newton method with R-order of convergence three at least is used to solve the nonlinear equations, and the HSS method is applied to approximately solve the Newton equations. For this class of inexact Newton methods, local and semilocal convergence theorems are proved under suitable conditions. Moreover, a globally convergent modified Newton-HSS method is introduced and a basic global convergence theorem is proved. Numerical results are given to confirm the effectiveness of our method. Hermitian and Skew-Hermitian splitting Newton-HSS method Large sparse systems Nonlinear equations Positive-definite Jacobian matrices Convergence analysis Chen, Minhong aut Enthalten in Numerical algorithms Springer US, 1991 64(2013), 4 vom: 18. Jan., Seite 659-683 (DE-627)130981753 (DE-600)1075844-6 (DE-576)029154111 1017-1398 nnns volume:64 year:2013 number:4 day:18 month:01 pages:659-683 https://doi.org/10.1007/s11075-012-9684-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 GBV_ILN_2088 AR 64 2013 4 18 01 659-683 |
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10.1007/s11075-012-9684-5 doi (DE-627)OLC2051162425 (DE-He213)s11075-012-9684-5-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Wu, Qingbiao verfasserin aut Convergence analysis of modified Newton-HSS method for solving systems of nonlinear equations 2013 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media New York 2013 Abstract Hermitian and skew-Hermitian splitting(HSS) method has been proved quite successfully in solving large sparse non-Hermitian positive definite systems of linear equations. Recently, by making use of HSS method as inner iteration, Newton-HSS method for solving the systems of nonlinear equations with non-Hermitian positive definite Jacobian matrices has been proposed by Bai and Guo. It has shown that the Newton-HSS method outperforms the Newton-USOR and the Newton-GMRES iteration methods. In this paper, a class of modified Newton-HSS methods for solving large systems of nonlinear equations is discussed. In our method, the modified Newton method with R-order of convergence three at least is used to solve the nonlinear equations, and the HSS method is applied to approximately solve the Newton equations. For this class of inexact Newton methods, local and semilocal convergence theorems are proved under suitable conditions. Moreover, a globally convergent modified Newton-HSS method is introduced and a basic global convergence theorem is proved. Numerical results are given to confirm the effectiveness of our method. Hermitian and Skew-Hermitian splitting Newton-HSS method Large sparse systems Nonlinear equations Positive-definite Jacobian matrices Convergence analysis Chen, Minhong aut Enthalten in Numerical algorithms Springer US, 1991 64(2013), 4 vom: 18. Jan., Seite 659-683 (DE-627)130981753 (DE-600)1075844-6 (DE-576)029154111 1017-1398 nnns volume:64 year:2013 number:4 day:18 month:01 pages:659-683 https://doi.org/10.1007/s11075-012-9684-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 GBV_ILN_2088 AR 64 2013 4 18 01 659-683 |
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10.1007/s11075-012-9684-5 doi (DE-627)OLC2051162425 (DE-He213)s11075-012-9684-5-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Wu, Qingbiao verfasserin aut Convergence analysis of modified Newton-HSS method for solving systems of nonlinear equations 2013 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media New York 2013 Abstract Hermitian and skew-Hermitian splitting(HSS) method has been proved quite successfully in solving large sparse non-Hermitian positive definite systems of linear equations. Recently, by making use of HSS method as inner iteration, Newton-HSS method for solving the systems of nonlinear equations with non-Hermitian positive definite Jacobian matrices has been proposed by Bai and Guo. It has shown that the Newton-HSS method outperforms the Newton-USOR and the Newton-GMRES iteration methods. In this paper, a class of modified Newton-HSS methods for solving large systems of nonlinear equations is discussed. In our method, the modified Newton method with R-order of convergence three at least is used to solve the nonlinear equations, and the HSS method is applied to approximately solve the Newton equations. For this class of inexact Newton methods, local and semilocal convergence theorems are proved under suitable conditions. Moreover, a globally convergent modified Newton-HSS method is introduced and a basic global convergence theorem is proved. Numerical results are given to confirm the effectiveness of our method. Hermitian and Skew-Hermitian splitting Newton-HSS method Large sparse systems Nonlinear equations Positive-definite Jacobian matrices Convergence analysis Chen, Minhong aut Enthalten in Numerical algorithms Springer US, 1991 64(2013), 4 vom: 18. Jan., Seite 659-683 (DE-627)130981753 (DE-600)1075844-6 (DE-576)029154111 1017-1398 nnns volume:64 year:2013 number:4 day:18 month:01 pages:659-683 https://doi.org/10.1007/s11075-012-9684-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 GBV_ILN_2088 AR 64 2013 4 18 01 659-683 |
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Convergence analysis of modified Newton-HSS method for solving systems of nonlinear equations |
| abstract |
Abstract Hermitian and skew-Hermitian splitting(HSS) method has been proved quite successfully in solving large sparse non-Hermitian positive definite systems of linear equations. Recently, by making use of HSS method as inner iteration, Newton-HSS method for solving the systems of nonlinear equations with non-Hermitian positive definite Jacobian matrices has been proposed by Bai and Guo. It has shown that the Newton-HSS method outperforms the Newton-USOR and the Newton-GMRES iteration methods. In this paper, a class of modified Newton-HSS methods for solving large systems of nonlinear equations is discussed. In our method, the modified Newton method with R-order of convergence three at least is used to solve the nonlinear equations, and the HSS method is applied to approximately solve the Newton equations. For this class of inexact Newton methods, local and semilocal convergence theorems are proved under suitable conditions. Moreover, a globally convergent modified Newton-HSS method is introduced and a basic global convergence theorem is proved. Numerical results are given to confirm the effectiveness of our method. © Springer Science+Business Media New York 2013 |
| abstractGer |
Abstract Hermitian and skew-Hermitian splitting(HSS) method has been proved quite successfully in solving large sparse non-Hermitian positive definite systems of linear equations. Recently, by making use of HSS method as inner iteration, Newton-HSS method for solving the systems of nonlinear equations with non-Hermitian positive definite Jacobian matrices has been proposed by Bai and Guo. It has shown that the Newton-HSS method outperforms the Newton-USOR and the Newton-GMRES iteration methods. In this paper, a class of modified Newton-HSS methods for solving large systems of nonlinear equations is discussed. In our method, the modified Newton method with R-order of convergence three at least is used to solve the nonlinear equations, and the HSS method is applied to approximately solve the Newton equations. For this class of inexact Newton methods, local and semilocal convergence theorems are proved under suitable conditions. Moreover, a globally convergent modified Newton-HSS method is introduced and a basic global convergence theorem is proved. Numerical results are given to confirm the effectiveness of our method. © Springer Science+Business Media New York 2013 |
| abstract_unstemmed |
Abstract Hermitian and skew-Hermitian splitting(HSS) method has been proved quite successfully in solving large sparse non-Hermitian positive definite systems of linear equations. Recently, by making use of HSS method as inner iteration, Newton-HSS method for solving the systems of nonlinear equations with non-Hermitian positive definite Jacobian matrices has been proposed by Bai and Guo. It has shown that the Newton-HSS method outperforms the Newton-USOR and the Newton-GMRES iteration methods. In this paper, a class of modified Newton-HSS methods for solving large systems of nonlinear equations is discussed. In our method, the modified Newton method with R-order of convergence three at least is used to solve the nonlinear equations, and the HSS method is applied to approximately solve the Newton equations. For this class of inexact Newton methods, local and semilocal convergence theorems are proved under suitable conditions. Moreover, a globally convergent modified Newton-HSS method is introduced and a basic global convergence theorem is proved. Numerical results are given to confirm the effectiveness of our method. © Springer Science+Business Media New York 2013 |
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Convergence analysis of modified Newton-HSS method for solving systems of nonlinear equations |
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https://doi.org/10.1007/s11075-012-9684-5 |
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Chen, Minhong |
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