論文リスト（テーマ別）

(論文リストに戻る )

　◆線形方程式 　◆固有値問題 　◆特殊行列
　◆行列方程式 　◆行列関数 　◆テンソル計算
　◆微分方程式 　◆量子計算 　◆最適化




●線形方程式

線形方程式の数値解法（クリロフ部分空間法）
◆ A. Imakura, T. Sogabe, S.-L. Zhang,
“A look-back-type restart for the restarted Krylov subspace methods for solving non-Hermitian linear systems”,
Japan J. Ind. Appl. Math., 35 (2018), pp. 835-859.
◆ C. Wen, T.-Z. Huang, T. Sogabe,
“An extension of two conjugate direction methods to Markov chain problems”,
Computing and Informatics, 34 (2015), pp. 1001-1022.
◆ X.-M. Gu, T.-Z. Huang, L. Li, H.-B. Li, T Sogabe, M. Clemens,
“Quasi-minimal residual variants of the COCG and COCR methods for complex symmetric linear systems in electromagnetic simulations”
IEEE Trans. Microw. Theory Techn., 62 (2014), pp. 2859-2867.
◆ 今倉暁，楊済栄，曽我部知広，張紹良，
“デフレーション型とLook-Back 型のリスタート を併用したGMRES(m) 法の収束特性”,
日本応用数理学会論文誌，Vol．22，No．3，2012，pp．117-141．
◆ 今倉暁，曽我部知広，張紹良，
“非対称線形方程式のためのLook-Back GMRES(m) 法”
日本応用数理学会論文誌，Vol．22，No．1，2012，pp. 1-21．
◆ A. Imakura, T. Sogabe, S.-L. Zhang，
“An efficient variant of the GMRES(m) method based on error equations”
East Asia J. on Appl. Math.., 2 (2012), pp. 19-32.
◆ L. Du, T. Sogabe, S.-L. Zhang,
“A variant of the IDR(s) method with quasi-minimal residual strategy”,
J. Comput. Appl. Math., 236 (2011), pp. 621-630.
◆ L. Du, T. Sogabe, S.-L. Zhang
“Quasi-minimal residual smoothing technique for the IDR(s) method”,
JSIAM Letters, 3 (2011), pp. 13-16.
◆ 今倉暁，曽我部知広，張紹良， 　 　　　　　　　 　
“GMRES(m)法のリスタートについて”，
日本応用数理学会論文誌，Vol．19，No．4，2009，pp．551-564．
◆ Y.-F. Jing, T.-Z. Huang, Y. Zhang, L. Li, G.-H. Cheng, Z.-G. Ren, Y. Duan, T. Sogabe, B. Carpentieri, 　　　　　　　
“Lanczos-type variants of the COCR method for complex nonsymmetric linear systems”,
J. Comput. Phys., 228 (2009), pp. 6376-6394.
◆ T. Sogabe, M. Sugihara, S.-L. Zhang, 　　　　　　　　　　　　　　　　
“An extension of the conjugate residual method to nonsymmetric linear systems”,
J. Comput. Appl. Math., 226 (2009), pp. 103-113.
◆ 南さつき，曽我部知広，杉原正顯，張紹良，
“Bi-CR法への準最小残差アプローチの適用について”，
日本応用数理学会論文誌，Vol．17，No．3，2007，pp．301-317．
◆ 阿部邦美，曽我部知広，藤野清次，張紹良，　　
“非対称行列用共役残差法に基づく積型反復解法”，
情報処理学会論文誌「コンピューティングシステム」，Vol．48，No．SIG 8 (ACS18)，2007，pp.11-21．
◆ T. Sogabe, S.-L. Zhang,
“A COCR method for solving complex symmetric linear systems”,
J. Comput. Appl. Math., 199 (2007), pp. 297-303.
◆ T. Sogabe, S.-L. Zhang, (Invited Paper)
“An iterative method based on an A-biorthogonalization process for nonsymmetric linear systems”,
in: Proceedings of The 7th China-Japan Seminar on Numerical Mathematics, ed. Z.-C. Shi and H. Okamoto,
Science Press, Beijing, 2006, pp. 120-130.
◆ 曽我部知広, 杉原正顯, 張紹良,
“共役残差法の非対称行列用への拡張”,
日本応用数理学会論文誌，Vol．15, No．3，2005，pp．445-459．
◆ T. Sogabe, S.-L. Zhang, (Invited Lecture)
“Extended conjugate residual methods for solving nonsymmetric linear systems”,
in: Numerical Linear Algebra and Optimization, ed. Y. Yuan, Science Press, Beijing/NewYork, 2004, pp. 88-99.
◆ 曽我部知広，金成海，阿部邦美，張紹良，
“CGS法の改良について”，
日本応用数理学会論文誌，Vol．14，No．1，2004，pp．1-12．



シフト線形方程式の数値解法と計算物理学への応用　
◆ R. Zhao, T. Sogabe, T. Kemmochi, S.-L. Zhang,
Shifted LOPBiCG: A locally orthogonal product-type method for solving nonsymmetric shifted linear systems based on Bi-CGSTAB,
Numer. Linear Algebra. Appl., 31(2024), e2538.
◆ T. Hoshi, M. Kawamura, K. Yoshimi, Y. Motoyama, T. Misawa, Y. Yamaji, S. Todo, N. Kawashima, T. Sogabe,
Kω -- Open-source library for the shifted Krylov subspace method,
Comput. Phys. Commun., 258 (2021), 107536.
◆ L. Du, T. Sogabe, S.-L. Zhang,
IDR(s) for solving shifted nonsymmetric linear systems,
J. Comput. Appl. Math., 274 (2015), pp. 35-43.
◆ X.-M. Gu, T.-Z. Huang, J. Meng, T. Sogabe, H.-B. Li, L. Li,
BiCR-type methods for families of shifted linear systems,
Comput. Math. Appl., 68 (2014), pp. 746-758.
◆ A. Imakura, T. Sogabe, S.-L. Zhang,
“An efficient variant of the restarted shifted GMRES for solving shifted linear systems”,
J. Math. Res. Appl., 33 (2013), pp. 127-141.
◆ T. Sogabe, T. Hoshi, S.-L. Zhang, T. Fujiwara,　　　　　　　 　　　　
“Solution of generalized shifted linear systems with complex symmetric matrices”,
J. Comput. Phys., 231(2012), pp. 5669-5684.
◆ H. Teng, T. Fujiwara, T. Hoshi, T. Sogabe, S.-L. Zhang, S. Yamamoto,
“Efficient and accurate linear algebraic methods for large-scale electronic structure calculations with non-orthogonal atomic orbitals”,
Phys. Rev. B 83, 165103 (2011), pp. 1-12.
◆ T. Sogabe and S.-L. Zhang,　　　　　　　 　　　　　　
“An extension of the COCR method to solving shifted linear systems with complex symmetric matrices”,
East Asia J. on Appl. Math., 1 (2011), pp. 97-107.
◆ T. Fujiwara, T. Hoshi, S. Yamamoto, T. Sogabe, S.-L. Zhang, 　　　　 　
“A novel algorithm of large-scale simultaneous linear equations”,
J. Phys.: Condens. Matter, 22 (2010), 074206, pp.1-6.
◆ 曽我部知広， 張紹良， 　　　
大規模シフト線形方程式の数値解法－クリロフ部分空間の性質に着目して－，
応用数理，Vol．19，No．3，2009，pp．27-42．　
◆ S. Yamamoto, T. Sogabe, T. Hoshi, S.-L. Zhang, T. Fujiwara, 　
“Shifted COCG method and its application to double orbital extended Hubbard model”,
J. Phys. Soc. Jpn., Vol. 77, No. 11, 114713 (2008), pp. 1-8. 　　　　　
◆ T. Sogabe, T. Hoshi, S.-L. Zhang, and T. Fujiwara, 　　　　　　
“On a weighted quasi-residual minimization strategy for solving complex symmetric shifted linear systems”, 　　　　　　　　　　　
Electron. Trans. Numer. Anal., 31 (2008), pp. 126-140.
◆ T. Sogabe, T. Hoshi, S.-L. Zhang, T. Fujiwara, (Invited Paper)
“A numerical method for calculating the Green's function arising from electronic structure theory”,
in: Frontiers of Computational Science, eds. Y. Kaneda, H. Kawamura and M. Sasai,
Springer-Verlag, Berlin/Heidelberg, 2007, pp. 189-195.
◆ R. Takayama, T. Hoshi, T. Sogabe, S.-L. Zhang, T. Fujiwara,　　
“Linear algebraic calculation of Green's function for large-scale electronic structure theory ”,
Phys. Rev. B 73, 165108 (2006), pp.1-9.


複数の右辺項を持つ線形方程式の数値解法（ブロック・クリロフ部分空間法）
◆ L. Du, T. Sogabe, B. Yu, Y. Yamamoto, S.-L. Zhang,
“A block IDR(s) method for nonsymmetric linear systems with multiple right-hand sides”,
J. Comput. Appl. Math., 235 (2011), pp. 4095-4106.


クリロフ部分空間法の前処理技術
◆ A. Imakura, T. Sogabe, S.-L. Zhang， 　　　　　　　 　
“An implicit wavelet sparse approximate inverse preconditioner using block finger pattern”,
Numer. Linear Algebra. Appl., 16 (2009), pp.915-928.
◆ 前田祥兵, 阿部邦美, 曽我部知広, 張紹良, 　　　　　　
“AOR法を用いた可変的前処理付き一般化共役残差法” 　　　　　　　　　　　　　
日本応用数理学会論文誌，Vol．18，No．1，2008，pp．155-170．
◆ 今倉暁，曽我部知広，張紹良， 　　　　　　 　　　　　　
“Finger patternのブロック化による陰的wavelet近似逆行列前処理の高速化”，　　　
日本応用数理学会論文誌，Vol．17，No．4，2007，pp．523-542．
◆ 曽我部知広，鄭波，橋本康，張紹良，
“非対称Toeplitz行列のための置換行列による前処理”， 　
日本応用数理学会論文誌，Vol．15，No．2, 2005，pp．159-168．


特殊な行列を係数に持つ線形方程式の数値解法
◆ J. Jia, T. Sogabe,
Generalized Sherman-Morrison-Woodbury formula based algorithm for the inverses of opposite-bordered tridiagonal matrices,
J. Math. Chem., 58 (2020), pp. 1466-1480.
◆ L. Du, T. Sogabe, S.-L. Zhang,
A fast algorithm for solving tridiagonal quasi-Toeplitz linear systems,
Appl. Math. Lett., 75 (2018), pp. 74-81.
◆ J. Jia, T. Sogabe, S. Li,
A generalized symbolic Thomas algorithm for the solution of opposite-bordered tridiagonal linear systems,
J. Comput. Appl. Math., 290 (2015), pp. 423-432.
◆ L. Du, T. Sogabe, S.-L. Zhang,
An algorithm for solving nonsymmetric penta-diagonal Toeplitz linear systems,
Appl. Math. Comput., 244 (2014) pp. 10-15.
◆ J. Jia, T. Sogabe,
“A novel algorithm for solving quasi penta-diagonal linear systems”，
J. Math. Chem., 51 (2013), pp. 881-889.
◆ J. Jia, T. Sogabe,
“A novel algorithm and its parallelization for solving nearly penta-diagonal linear systems”,
Int. J. Comput. Math., 90 (2013), pp. 435-444.
◆ J. Jia, Q. Kong, T. Sogabe,
“A fast numerical algorithm for solving nearly penta-diagonal linear systems”,
Int. J. Comput. Math., 89 (2012), pp. 851-860.
◆ J. Jia, Q. Kong, T. Sogabe,
“A new algorithm for solving nearly penta-diagonal Toeplitz linear systems“
Comput. Math. Appl., 63 (2012), pp. 1238-1243.
◆ T. Sogabe, 　　　　　　　　　　　　　　　　
“New algorithms for solving periodic tridiagonal and periodic pentadiagonal linear systems”,
Appl. Math. Comput., 202 (2008), pp. 850-856.
◆ T. Sogabe,　　　　　　　 　　　　　　
“Numerical algorithms for solving comrade linear systems based on tridiagonal solvers”,
Appl. Math. Comput., 198 (2008), pp. 117-122.


●固有値問題

固有値問題・特異値問題の数値解法と計算物理学への応用
◆ K.-I. Ishikawa, T. Sogabe,
A thick-restart Lanczos type method for Hermitian J-symmetric eigenvalue problems,
Japan J. Ind. Appl. Math., 38 (2021), pp. 233-256.
◆ 李東珍，曽我部知広，宮武勇登，張紹良，
“指定番目の特異値と特異ベクトルの計算について＂，　　
日本応用数理学会論文誌，Vol．29，No．1，2019，pp. 121-140．
◆ D. Lee, T. Hoshi, T. Sogabe, Y. Miyatake, S.-L. Zhang,
“Solution of the k-th eigenvalue problem in large-scale electronic structure calculations”,
J. Comput. Phys., 371 (2018), pp. 618-632.
◆ K. Ooi, Y. Mizuno, T. Sogabe, Y. Yamamoto, S.-L. Zhang,
“Solution of a nonlinear eigenvalue problem using signed singular values”,
East Asia J. on Appl. Math., 7 (2018), pp. 799-809.
◆ D. J. Lee, T. Miyata, T. Sogabe, T. Hoshi, S.-L. Zhang,
“An interior eigenvalue problem from electronic structure calculations”,
Japan J. Ind. Appl. Math., 30 (2013), pp. 625-633.
◆ T. Hoshi, S. Yamamoto, T. Fujiwara, T. Sogabe, S.-L. Zhang,
“An order-N electronic structure theory with generalized eigen-value equations and its application to a ten-million-atom system”,
J. Phys.: Condens. Matter 24 (2012) 165502, pp. 1-5.
◆ 山下達也，宮田考史，曽我部知広，星健夫，藤原毅夫，張紹良，
“一般化固有値問題に対するArnoldi(M,W,G)法”，
日本応用数理学会論文誌，Vol．21，No．3，2011，pp. 241-254．
◆ Y. Mizuno, K. Ohi, T. Sogabe, Y. Yamamoto, Y. Kaneda,　
“Four-point correlation function of a passive scalar field in rapidly fluctuating turbulence: Numerical analysis of an exact closure equation ”,
Phys. Rev. E 82, 036316 (2010), pp.1-9.
◆ 宮田考史，曽我部知広，張紹良，
“Jacobi-Davidson 法における修正方程式の解法 －射影空間における Krylov 部分空間のシフト不変性に基づいて－ ”，
日本応用数理学会論文誌，Vol．20，No．2，2010，pp. 115-129．
◆ 宮田考史，杜磊，曽我部知広，山本有作，張紹良，
“多重連結領域の固有値問題に対する Sakurai-Sugiura 法の拡張”，
日本応用数理学会論文誌，Vol．19，No．4，2009，pp．537-550．


●特殊行列

行列式、パーマネント、パフィアン
◆ F. Yilmaz, T. Sogabe, E. Kirklar,
On the pfaffians and determinants of some skew-centrosymmetric matrices,
J. Integer Sequences, 20 (2017), pp. 1-9.
◆ C. M. da Fonseca, T. Sogabe, F. Yilmaz,
“Lower k-Hessenberg matrices and k-Fibonacci, Fibonacci-p and Pell (p,i) numbers”,
Gen. Math. Notes, 31 (2015), pp. 10-17.
◆ T. Sogabe,
“A note on “A fast numerical algorithm for the determinant of a pentadiagonal matrix””,
Appl. Math. Comput., 201 (2008), pp. 561-564.
◆ T. Sogabe,
“A fast numerical algorithm for the determinant of a pentadiagonal matrix”,
Appl. Math. Comput., 196 (2008), pp. 835-841.
◆ T. Sogabe,　　
“On a two-term recurrence for the determinant of a general matrix”,
Appl. Math. Comput., 187 (2007), pp. 785-788.


基本対称式の性質
◆ M.E.A. El-Mikkawy, T. Sogabe,
“Notes on particular symmetric polynomials with applications”,
Appl. Math. Comput., 215 (2010), pp. 3311-3317.
◆ T. Sogabe, M.E.A. El-Mikkawy， 　　　　　　　 　　　　
“On a problem related to the Vandermonde determinant”
Discrete Appl. Math., 157 (2009), pp. 2997-2999.


k-3重対角行列の性質 （実数体 & 有限体上)
◆ S. Takahira, T. Sogabe, T. S. Usuda,
Bidiagonalization of (k, k + 1)-tridiagonal matrices,
Special Matrices, 7 (2019), pp. 20-26.
◆ A. Ohashi, T. Sogabe, T. S. Usuda,
Fast block diagonalization of (k, k')-pentadiagonal matrices,
Int. J. Pure and Appl. Math. 106 (2016), pp. 513-523.
◆ A. Ohashi, T. Sogabe, T.S. Usuda,
On decomposition of k-tridiagonal l-Toeplitz matrices and its applications,
Special Matrices, 3 (2015), pp. 200-206.
◆ T. Sogabe and F. Yilmaz,
“A note on a fast breakdown-free algorithm for computing the determinants and the permanents of k-tridiagonal matrices”,
Appl. Math. Comput., 249 (2014) pp. 98-102.
◆ F. Yilmaz, T. Sogabe,
“A note on symmetric k-tridiagonal matrix family and the Fibonacci numbers”,
Int. J. Pure and Appl. Math., 96 (2014), pp. 289-298.
◆ J. Jia, T. Sogabe, M.E.A. El-Mikkawy,
“Inversion of k-tridiagonal matrices with Toeplitz structure”
Comput. Math. Appl., 65 (2013), pp. 116-125
◆ T. Sogabe, M.E.A. El-Mikkawy,
“Fast block diagonalization of k-tridiagonal matrices”,
Appl. Math. Comput., 218 (2011), pp. 2740-2743.
◆ M.E.A. El-Mikkawy, T. Sogabe,
“A new family of k-Fibonacci numbers”,
Appl. Math. Comput. 215 (2010), pp. 4456-4461.


●行列方程式

行列方程式
◆ Y. Satake, T. Sogabe, T. Kemmochi, S.-L. Zhang,
“Matrix equation representation of the convolution equation and its unique solvability”,
Special Matrices (accepted)
◆ Y. Satake, T. Sogabe, T. Kemmochi, S.-L. Zhang,
“On a transformation of the *-congruence Sylvester equation for the least squares optimization”,
Optim. Methods & Softw., 35 (2020), pp. 974-981.
◆ Y. Satake, M. Oozawa, T. Sogabe, Y. Miyatake, T. Kemmochi, S.-L. Zhang,
Relation between the T-congruence Sylvester equation and the generalized Sylvester equation,
Appl. Math. Lett., 96 (2019), pp. 7-13.
◆ M. Oozawa, T. Sogabe, Y. Miyatake, S.-L. Zhang,
On a relationship between the T-congruence sylvester equation and the Lyapunov equation,
J. Comput. Appl. Math., 329 (2018), pp. 51-56.


●行列関数

行列関数（行列平方根、行列p乗根、行列実数乗、行列対数関数）
◆ F. Tatsuoka, T. Sogabe, T. Kemmochi, S.-L. Zhang,
Computing the matrix exponential with the double exponential formula,
Special Matrices (accepted)
◆ F. Tatsuoka, T. Sogabe, Y. Miyatake, T. Kemmochi, S.-L. Zhang,
Computing the matrix fractional power based on the double exponential formula,
Electron. Trans. Numer. Anal., 54 (2021), pp. 558-580.
◆ 立岡文理，曽我部知広，張紹良，
数値積分に基づく行列実数乗の計算について，
計算数理工学レビュー, Vol. 2019-2 (2019), pp. 45-55.
◆ F. Tatsuoka, T. Sogabe, Y. Miyatake, S.-L. Zhang,
“Algorithms for the computation of the matrix logarithm based on the double exponential formula”,
J. Comput. Appl. Math., 373 (2020), 112396.
◆ 立岡文理，曽我部知広，宮武勇登，張紹良，
二重指数関数型数値積分公式を用いた行列実数乗の計算，
日本応用数理学会論文誌，Vol．28，No．3，2018，pp. 142-161．
◆ F. Tatsuoka, T. Sogabe, Y. Miyatake, S.-L. Zhang
A cost-efficient variant of the incremental Newton iteration for the matrix pth root,
J. Math. Res. Appl. 37 (2017), pp. 97-106.
◆ S. Mizuno, Y. Moriizumi, T. S. Usuda, T. Sogabe,
An initial guess of Newton's method for the matrix square root based on a sphere constrained optimization problem,
JSIAM Letters, 8 (2016), pp. 17-20.


●テンソル計算

数値多重線形代数（テンソル計算・テンソル積）
◆ J. Niu, T. Sogabe, L. Du, T. Kemmochi, S.-L. Zhang,
Tensor product-type methods for solving Sylvester tensor equations,
Appl. Math. Compute, 457 (2023), 128155.
◆ A. Ohashi, T. Sogabe,
Recent development for computing singular values of a generalized tensor sum,
J. Adv. Simul. Sci. Eng. (JASSE), 9 (2022), pp. 136-149.
◆ A. Ohashi, T. Sogabe,
Numerical algorithms for computing an arbitrary singular value of a tensor sum,
Axioms 10 (2021), 211. (14pp.)
◆ A. Ohashi, T. Sogabe
“On computing the minimum singular value of a tensor sum”,
Special Matrices, 7 (2019), pp. 95-106.
◆ A. Ohashi, T. Sogabe,
“On computing maximum/minimum singular values of a generalized tensor sum”,
Electron. Trans. Numer. Anal., 43 (2015), pp. 244-254.
◆ A. Ohashi, T. S. Usuda, T. Sogabe, F. Yilmaz,
“On tensor product decomposition of k-tridiagonal Toeplitz matrices”,
Int. J. Pure and Appl. Math., 103 (2015), pp. 537-545.


●微分方程式

微分方程式の（数値）解法
◆ E. Miyazaki, T. Kemmochi, T. Sogabe, S.-L. Zhang,
"A structure-preserving numerical method for the fourth-order geometric evolution equations for planar curves",
Commun. Math. Res., 39 (2023), pp. 296-330.
◆ K. Nakano, T. Kemmochi, Y. Miyatake, T. Sogabe, S.-L. Zhang,
“Modified Strang splitting for semilinear parabolic problems”,
JSIAM Letters, 11 (2019), pp. 77-80.
◆ Y. Miyatake, T. Nakagawa, T. Sogabe, S.-L. Zhang,
“A structure-preserving Fourier pseudo-spectral linearly implicit scheme for the space-fractional nonlinear Schrödinger equation”,
J. Comput. Dyn., 6 (2019), pp. 361-383.
◆ Y. Miyatake, G. Eom, T. Sogabe, S.-L. Zhang,
“Energy-preserving H1-Galerkin schemes for the Hunter-Saxton equation”,
J. Math. Res. Appl. 37 (2017), pp. 107-118.
◆ J. Jia, T. Sogabe,
“On particular solution of ordinary differential equations with constant coefficients”,
Appl. Math. Comput., 219 (2013), pp. 6761-6767.


微分方程式の数値解法（離散勾配法）と線形方程式の数値解法（定常反復法）との関係
◆ Y. Miyatake, T. Sogabe, S.-L. Zhang,
“Adaptive SOR methods based on the Wolfe conditions”,
Numer. Algorithms, 84 (2020), pp. 117-132.
◆ Y. Miyatake, T. Sogabe, S.-L. Zhang,
“On the equivalence between SOR-type methods for linear systems and the discrete gradient methods for gradient systems”,
J. Comput. Appl. Math., 342 (2018), pp. 58-69.
◆ 宮武勇登, 曽我部知広, 張紹良,
“微分方程式に対する離散勾配法に基づく線形方程式の数値解法の生成”,
日本応用数理学会論文誌，Vol．27，No．3, 2017, pp. 239-249.


●量子計算

量子アルゴリズム
◆ S. Takahira, A. Ohashi, T. Sogabe, T. S. Usuda,
“Quantum algorithms based on the block-encoding framework for matrix functions by contour integrals”,
Quantum Inform. Comput., 22 (2022), pp. 965-979.
◆ S. Takahira, A. Ohashi, T. Sogabe, T. S. Usuda,
“Quantum algorithm for matrix functions by Cauchy's integral formula”,
Quantum Inform. Comput., 20:1-2 (2020), pp. 14-36.


●最適化

二次計画問題（球面制約上，非負制約上）
◆ Y. Miyatake and T. Sogabe,
“Adaptive projected SOR algorithms for nonnegative quadratic programming”,
Japan J. Ind. Appl. Math., (accepted)
◆ T. Sogabe, A. Suzuki, S.-L. Zhang,
“An implicit evaluation method of vector 2-norms arising from sphere constrained quadratic optimizations ”,
CSIAM Trans. Appl. Math., 1 (2020), pp. 142-154 (Invited)