2 参考文献および参考書の記述
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開始行:
[[1 線形方程式の解法の選択]]&br;
2 参考文献および参考書の記述
#contents
---------------------------------------------
|~ 解法 |~ 原著論文 |CENTER:~ ★|CENTER:~ 教|CENTER:~ 科|C...
|~|~|CENTER:~ [[[2]>#No2]] |CENTER:~ [[[14]>#No14]] |CENT...
| [[CG 法]] |CENTER: [[[10]>#No10]] |CENTER: 14–17 |CENTE...
| [[CR 法]] |CENTER: [[[22]>#No22]] |CENTER: ― |CENTER: 1...
| [[MINRES 法]] |CENTER: [[[12]>#No12]] |CENTER: 17–18 |C...
| [[GMRES 法]], [[GMRES(m) 法]] |CENTER: [[[15]>#No15]] |...
| [[GCR 法]], [[GCR(m) 法]], [[ORTHOMIN(m) 法]] |CENTER: ...
| [[FOM 法]], [[FOM(m) 法]] |CENTER: [[[13]>#No13]] |CENT...
| [[DQGMRES(m) 法]] |CENTER: [[[16]>#No16]] |CENTER: ― |C...
| [[GMRES-DR(m; k) 法]] |CENTER: [[[11]>#No11]] |CENTER: ...
| [[Look-Back GMRES(m) 法]] |CENTER: [?] |CENTER: ― |CENT...
| [[Bi-CG 法]] |CENTER: [[[6]>#No6]] |CENTER: 21–23 |CENT...
| [[Bi-CR 法]] |CENTER: [[[18]>#No18]], [[[19]>#No19]] |C...
| [[QMR 法]] |CENTER: [[[8]>#No8]] |CENTER: 23–25 |CENTER...
| [[CGS 法]] |CENTER: [[[20]>#No20]] |CENTER: 25–27 |CENT...
| [[Bi-CGSTAB 法]] |CENTER: [[[26]>#No26]] |CENTER: 27–28...
| [[Bi-CGSTAB2 法]] |CENTER: [[[9]>#No9]] |CENTER: ― |CEN...
| [[Bi-CGSTAB(l) 法]] |CENTER: [[[17]>#No17]] |CENTER: ― ...
| [[GPBi-CG 法]] |CENTER: [[[28]>#No28]] |CENTER: ― |CENT...
| [[CRS 法]], [[Bi-CRSTAB 法]], [[GPBi-CR 法]] |CENTER: [...
| [[TFQMR 法]] |CENTER: [[[7]>#No7]] |CENTER: ― |CENTER: ...
| [[QMRCGSTAB 法]] |CENTER: [[[3]>#No3]] |CENTER: ― |CENT...
| [[QMRCGSTAB(l) 法]] |CENTER: [[[25]>#No25]] |CENTER: ― ...
| [[IDR(s) 法]] |CENTER: [[[21]>#No21]] |CENTER: ― |CENTE...
| [[GBi-CGSTAB(s; l) 法]] |CENTER: [[[24]>#No24]] |CENTER...
| [[Jacobi 法]], [[Gauss-Seidel 法]], [[SOR 法]] |CENTER:...
| [[AOR 法]] |CENTER: ― |CENTER:― |CENTER: ― |CENTER: ― |...
| [[ADI 法]] |CENTER: ― |CENTER:― |CENTER: 124–126 |CENTE...
| [[減速定常反復法]] |CENTER: ― |CENTER:― |CENTER: ― |CEN...
| [[Chebyshev 加速]] |CENTER: ― |CENTER:― |CENTER: ― |CEN...
| [[CGNE 法]] |CENTER: [[[4]>#No4]] |CENTER: 18 |CENTER: ...
| [[CGNR 法]] |CENTER: [[[10]>#No10]] |CENTER: 18 |CENTER...
| [[Cimmino-NR 法]] |CENTER: ― |CENTER:― |CENTER: 249–251...
| [[幾何的マルチグリッド法]]&br;[[代数的マルチグリッド法]...
| [[COCG 法]] |CENTER: ― |CENTER:― |CENTER: ― |CENTER: 10...
| [[COCR 法]] |CENTER: ― |CENTER:― |CENTER: ― |CENTER: ― ...
| [[QMR-SYM 法]] |CENTER: ― |CENTER:― |CENTER: ― |CENTER:...
| [[Uzawa 法]] |CENTER: ― |CENTER:― |CENTER: 254–257 |CEN...
| [[FFT に基づく高速解法(直接法)]] |CENTER: ― |CENTER:― |...
---------------------------------------------
*参考文献 [#s9be51f8]
&aname(No1){[1]}; Kuniyoshi Abe, Tomohiro Sogabe, Seiji F...
subspace method based on conjugate residual method for no...
IPSJ Transactions on Advanced Computing Systems 2007; 48(...
&aname(No2){[2]}; Richard Barrett, Michael W. Berry, Tony...
Victor Eijkhout, Roldan Pozo, Charles Romine and Henk A. ...
Solution of Linear Systems: Building Blocks for Iterative...
1993.
&aname(No3){[3]}; Tony F. Chan, Efstratios Gallopoulos, V...
quasi-minimal residual variant of the Bi-CGSTAB algorithm...
Journal on Scientific Computing 1994; 15(2):338–347.
&aname(No4){[4]}; Edward J. Craig, The N-step iteration p...
34:64–73.
&aname(No5){[5]}; Stanley C. Eisenstat, Howard C. Elman a...
for nonsymmetric systems of linear equations, SIAM Journa...
20(2):345–357.
&aname(No6){[6]}; Roger Fletcher, Conjugate gradient meth...
G. Alistair Watros (ed.), vol. 506, Springer-Verlag: New ...
&aname(No7){[7]}; Roland W. Freund, A transpose-free quas...
systems, SIAM Journal on Scientific Computing 1993; 14(2)...
&aname(No8){[8]}; Roland W. Freund and No¨el M. Nachtigal...
Hermitian linear systems, Numerische Mathematik 1991; 60(...
&aname(No9){[9]}; Martin H. Gutknecht, Variants of BiCGSt...
on Scientific Computing 1993; 14(5):1020–1033.
&aname(No10){[10]}; Magnes R. Hestenes and Eduard Stiefel...
Journal of Research of the National Bureau of Standards 1...
&aname(No11){[11]}; Ronald B. Morgan, GMRES with deflated...
2002; 24(1):20–37.
&aname(No12){[12]}; Christopher C. Paige and Michael A. S...
equations, SIAM Journal on Numerical Analysis 1975; 12(4)...
&aname(No13){[13]}; Yousef Saad, Krylov subspace methods ...
of Computation 1981; 37(155):105–126.
&aname(No14){[14]}; Yousef Saad, Iterative Methods for Sp...
2003.
&aname(No15){[15]}; Yousef Saad and Martin H. Schultz, GM...
7(3):856–869.
&aname(No16){[16]}; Yousef Saad and Kesheng Wu, DQGMRES: ...
incomplete orthogonalization, Numerical Linear Algebra wi...
&aname(No17){[17]}; Gerard L. G. Sleijpen and Diederik R....
unsymmetric matrices with complex spectrum, Electronic Tr...
1993; 1:11–32.
&aname(No18){[18]}; Tomohiro Sogabe, Masaaki Sugihara and...
method for solving nonsymmetric linear systems, Transacti...
and Applied Mathematics 2005; 15(3):445–459, (in Japanese).
&aname(No19){[19]}; Tomohiro Sogabe, Masaaki Sugihara and...
method to nonsymmetric linear systems, Journal of Computa...
2009; 226(1):103–113.
&aname(No20){[20]}; Peter Sonneveld, CGS, a fast Lanczos-...
on Scientific and Statistical Computing 1989; 10(1):36–52.
&aname(No21){[21]}; Peter Sonneveld and Martin B. van Gij...
solving large nonsymmetric systems of linear equations, S...
2008; 31(2):1035–1062.
&aname(No22){[22]}; Eduard Stiefel, Relaxationsmethoden b...
Commentarii Mathematici Helvetici 1952; 29(1):157–179.
&aname(No23){[23]}; Masaaki Sugihara and Kazuo Murota, Th...
Tokyo, 2009, (in Japanese).
&aname(No24){[24]}; Masaaki Tanio and Masaaki Sugihara, G...
polynomials, Journal of Computational and Applied Mathema...
&aname(No25){[25]}; Charles H. Tong, A family of quasi-mi...
SIAM Journal on Scientific Computing 1994; 15(1):89–105.
&aname(No26){[26]}; Henk A. van der Vorst, Bi-CGSTAB: a f...
solution of nonsymmetric linear systems, SIAM Journal on ...
1992; 13(2):631–644.
&aname(No27){[27]}; Henk A. van der Vorst, Iterative Kryl...
Press: New York, NY, 2003.
&aname(No28){[28]}; Shao-Liang Zhang, GPBi-CG: generalize...
nonsymmetric linear systems, SIAM Journal on Scientific C...
&aname(No29){[29]}; 藤野 清次, 張 紹良, 反復法の数理 (応...
終了行:
[[1 線形方程式の解法の選択]]&br;
2 参考文献および参考書の記述
#contents
---------------------------------------------
|~ 解法 |~ 原著論文 |CENTER:~ ★|CENTER:~ 教|CENTER:~ 科|C...
|~|~|CENTER:~ [[[2]>#No2]] |CENTER:~ [[[14]>#No14]] |CENT...
| [[CG 法]] |CENTER: [[[10]>#No10]] |CENTER: 14–17 |CENTE...
| [[CR 法]] |CENTER: [[[22]>#No22]] |CENTER: ― |CENTER: 1...
| [[MINRES 法]] |CENTER: [[[12]>#No12]] |CENTER: 17–18 |C...
| [[GMRES 法]], [[GMRES(m) 法]] |CENTER: [[[15]>#No15]] |...
| [[GCR 法]], [[GCR(m) 法]], [[ORTHOMIN(m) 法]] |CENTER: ...
| [[FOM 法]], [[FOM(m) 法]] |CENTER: [[[13]>#No13]] |CENT...
| [[DQGMRES(m) 法]] |CENTER: [[[16]>#No16]] |CENTER: ― |C...
| [[GMRES-DR(m; k) 法]] |CENTER: [[[11]>#No11]] |CENTER: ...
| [[Look-Back GMRES(m) 法]] |CENTER: [?] |CENTER: ― |CENT...
| [[Bi-CG 法]] |CENTER: [[[6]>#No6]] |CENTER: 21–23 |CENT...
| [[Bi-CR 法]] |CENTER: [[[18]>#No18]], [[[19]>#No19]] |C...
| [[QMR 法]] |CENTER: [[[8]>#No8]] |CENTER: 23–25 |CENTER...
| [[CGS 法]] |CENTER: [[[20]>#No20]] |CENTER: 25–27 |CENT...
| [[Bi-CGSTAB 法]] |CENTER: [[[26]>#No26]] |CENTER: 27–28...
| [[Bi-CGSTAB2 法]] |CENTER: [[[9]>#No9]] |CENTER: ― |CEN...
| [[Bi-CGSTAB(l) 法]] |CENTER: [[[17]>#No17]] |CENTER: ― ...
| [[GPBi-CG 法]] |CENTER: [[[28]>#No28]] |CENTER: ― |CENT...
| [[CRS 法]], [[Bi-CRSTAB 法]], [[GPBi-CR 法]] |CENTER: [...
| [[TFQMR 法]] |CENTER: [[[7]>#No7]] |CENTER: ― |CENTER: ...
| [[QMRCGSTAB 法]] |CENTER: [[[3]>#No3]] |CENTER: ― |CENT...
| [[QMRCGSTAB(l) 法]] |CENTER: [[[25]>#No25]] |CENTER: ― ...
| [[IDR(s) 法]] |CENTER: [[[21]>#No21]] |CENTER: ― |CENTE...
| [[GBi-CGSTAB(s; l) 法]] |CENTER: [[[24]>#No24]] |CENTER...
| [[Jacobi 法]], [[Gauss-Seidel 法]], [[SOR 法]] |CENTER:...
| [[AOR 法]] |CENTER: ― |CENTER:― |CENTER: ― |CENTER: ― |...
| [[ADI 法]] |CENTER: ― |CENTER:― |CENTER: 124–126 |CENTE...
| [[減速定常反復法]] |CENTER: ― |CENTER:― |CENTER: ― |CEN...
| [[Chebyshev 加速]] |CENTER: ― |CENTER:― |CENTER: ― |CEN...
| [[CGNE 法]] |CENTER: [[[4]>#No4]] |CENTER: 18 |CENTER: ...
| [[CGNR 法]] |CENTER: [[[10]>#No10]] |CENTER: 18 |CENTER...
| [[Cimmino-NR 法]] |CENTER: ― |CENTER:― |CENTER: 249–251...
| [[幾何的マルチグリッド法]]&br;[[代数的マルチグリッド法]...
| [[COCG 法]] |CENTER: ― |CENTER:― |CENTER: ― |CENTER: 10...
| [[COCR 法]] |CENTER: ― |CENTER:― |CENTER: ― |CENTER: ― ...
| [[QMR-SYM 法]] |CENTER: ― |CENTER:― |CENTER: ― |CENTER:...
| [[Uzawa 法]] |CENTER: ― |CENTER:― |CENTER: 254–257 |CEN...
| [[FFT に基づく高速解法(直接法)]] |CENTER: ― |CENTER:― |...
---------------------------------------------
*参考文献 [#s9be51f8]
&aname(No1){[1]}; Kuniyoshi Abe, Tomohiro Sogabe, Seiji F...
subspace method based on conjugate residual method for no...
IPSJ Transactions on Advanced Computing Systems 2007; 48(...
&aname(No2){[2]}; Richard Barrett, Michael W. Berry, Tony...
Victor Eijkhout, Roldan Pozo, Charles Romine and Henk A. ...
Solution of Linear Systems: Building Blocks for Iterative...
1993.
&aname(No3){[3]}; Tony F. Chan, Efstratios Gallopoulos, V...
quasi-minimal residual variant of the Bi-CGSTAB algorithm...
Journal on Scientific Computing 1994; 15(2):338–347.
&aname(No4){[4]}; Edward J. Craig, The N-step iteration p...
34:64–73.
&aname(No5){[5]}; Stanley C. Eisenstat, Howard C. Elman a...
for nonsymmetric systems of linear equations, SIAM Journa...
20(2):345–357.
&aname(No6){[6]}; Roger Fletcher, Conjugate gradient meth...
G. Alistair Watros (ed.), vol. 506, Springer-Verlag: New ...
&aname(No7){[7]}; Roland W. Freund, A transpose-free quas...
systems, SIAM Journal on Scientific Computing 1993; 14(2)...
&aname(No8){[8]}; Roland W. Freund and No¨el M. Nachtigal...
Hermitian linear systems, Numerische Mathematik 1991; 60(...
&aname(No9){[9]}; Martin H. Gutknecht, Variants of BiCGSt...
on Scientific Computing 1993; 14(5):1020–1033.
&aname(No10){[10]}; Magnes R. Hestenes and Eduard Stiefel...
Journal of Research of the National Bureau of Standards 1...
&aname(No11){[11]}; Ronald B. Morgan, GMRES with deflated...
2002; 24(1):20–37.
&aname(No12){[12]}; Christopher C. Paige and Michael A. S...
equations, SIAM Journal on Numerical Analysis 1975; 12(4)...
&aname(No13){[13]}; Yousef Saad, Krylov subspace methods ...
of Computation 1981; 37(155):105–126.
&aname(No14){[14]}; Yousef Saad, Iterative Methods for Sp...
2003.
&aname(No15){[15]}; Yousef Saad and Martin H. Schultz, GM...
7(3):856–869.
&aname(No16){[16]}; Yousef Saad and Kesheng Wu, DQGMRES: ...
incomplete orthogonalization, Numerical Linear Algebra wi...
&aname(No17){[17]}; Gerard L. G. Sleijpen and Diederik R....
unsymmetric matrices with complex spectrum, Electronic Tr...
1993; 1:11–32.
&aname(No18){[18]}; Tomohiro Sogabe, Masaaki Sugihara and...
method for solving nonsymmetric linear systems, Transacti...
and Applied Mathematics 2005; 15(3):445–459, (in Japanese).
&aname(No19){[19]}; Tomohiro Sogabe, Masaaki Sugihara and...
method to nonsymmetric linear systems, Journal of Computa...
2009; 226(1):103–113.
&aname(No20){[20]}; Peter Sonneveld, CGS, a fast Lanczos-...
on Scientific and Statistical Computing 1989; 10(1):36–52.
&aname(No21){[21]}; Peter Sonneveld and Martin B. van Gij...
solving large nonsymmetric systems of linear equations, S...
2008; 31(2):1035–1062.
&aname(No22){[22]}; Eduard Stiefel, Relaxationsmethoden b...
Commentarii Mathematici Helvetici 1952; 29(1):157–179.
&aname(No23){[23]}; Masaaki Sugihara and Kazuo Murota, Th...
Tokyo, 2009, (in Japanese).
&aname(No24){[24]}; Masaaki Tanio and Masaaki Sugihara, G...
polynomials, Journal of Computational and Applied Mathema...
&aname(No25){[25]}; Charles H. Tong, A family of quasi-mi...
SIAM Journal on Scientific Computing 1994; 15(1):89–105.
&aname(No26){[26]}; Henk A. van der Vorst, Bi-CGSTAB: a f...
solution of nonsymmetric linear systems, SIAM Journal on ...
1992; 13(2):631–644.
&aname(No27){[27]}; Henk A. van der Vorst, Iterative Kryl...
Press: New York, NY, 2003.
&aname(No28){[28]}; Shao-Liang Zhang, GPBi-CG: generalize...
nonsymmetric linear systems, SIAM Journal on Scientific C...
&aname(No29){[29]}; 藤野 清次, 張 紹良, 反復法の数理 (応...
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