Krylov Subspace Methods for Linear Systems —Principles of Algorithms
Spiringer Series in Computational Mathematics, Springer, 2023．
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F. Tatsuoka, T. Sogabe, T. Sogabe, S.-L. Zhang, “A preconditioning technique of Gauss-Legendre quadrature for the logarithm of symmetric positive definite matrices”, To appear in Appl. Math. Lett. |
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J. Niu, L. Du, T. Sogabe, S.-L. Zhang, “A tensor Alternating Anderson-Richardson method for solving multilinear systems with M-tensors”, J. Comput. Appl. Math., 461 (2025), 116419 |
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Y. Miyatake and T. Sogabe, “Adaptive projected SOR algorithms for nonnegative quadratic programming”, Japan J. Ind. Appl. Math., 42 (2025), pp. 373-397 |
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F. Tatsuoka, T. Sogabe, T. Kemmochi, S.-L. Zhang, “Computing the matrix exponential with the double exponential formula”, Special Matrices, 12(2024), 20240013. |
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Y. Satake, T. Sogabe, T. Kemmochi, S.-L. Zhang, “Matrix equation representation of the convolution equation and its unique solvability”, Special Matrices, 12(2024), 20240001 |
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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. |
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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. |
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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. |
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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. |
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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. |
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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. |
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A. Ohashi, T. Sogabe, “Numerical algorithms for computing an arbitrary singular value of a tensor sum”, Axioms 10 (2021), 211. (14pp.) |
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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. |
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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. |
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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. |
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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) |
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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. |
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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. |
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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. |
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Y. Miyatake, T. Sogabe, S.-L. Zhang, “Adaptive SOR methods based on the Wolfe conditions”, Numer. Algorithms, 84 (2020), pp. 117-132. |
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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. |
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A. Ohashi, T. Sogabe, “On computing the minimum singular value of a tensor sum”, Special Matrices, 7 (2019), pp. 95-106. |
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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. |
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S. Takahira, T. Sogabe, T. S. Usuda, “Bidiagonalization of (k, k + 1)-tridiagonal matrices”, Special Matrices, 7 (2019), pp. 20-26. |
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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. |
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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. |
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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. |
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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. |
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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. |
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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. |
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F. Yilmaz, T. Sogabe, E. Kirklar, “On the pfaffians and determinants of some skew-centrosymmetric matrices”, J. Integer Sequences, 20 (2017), pp. 1-9. |
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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. |
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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. |
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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. |
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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. |
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A. Ohashi, T. Sogabe, “On computing maximum/minimum singular values of a generalized tensor sum”, Electron. Trans. Numer. Anal., 43 (2015), pp. 244-254. |
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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. |
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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. |
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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. |
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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. |
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L. Du, T. Sogabe, S.-L. Zhang, “IDR(s) for solving shifted nonsymmetric linear systems”, J. Comput. Appl. Math., 274 (2015), pp. 35-43. |
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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. |
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T. Sogabe, 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. |
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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. |
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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. |
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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. |
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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 |
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J. Jia, T. Sogabe, “On particular solution of ordinary differential equations with constant coefficients”, Appl. Math. Comput., 219 (2013), pp. 6761-6767. |
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J. Jia, T. Sogabe, “A novel algorithm for solving quasi penta-diagonal linear systems”， J. Math. Chem., 51 (2013), pp. 881-889. |
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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. |
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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 |
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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. |
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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. |
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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. |
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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. |
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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. |
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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. |
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T. Sogabe, M.E.A. El-Mikkawy, “Fast block diagonalization of k-tridiagonal matrices”, Appl. Math. Comput., 218 (2011), pp. 2740-2743. |
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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. |
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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. |
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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. |
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T. Sogabe, 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. |
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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. |
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M.E.A. El-Mikkawy, T. Sogabe, “A new family of k-Fibonacci numbers”, Appl. Math. Comput. 215 (2010), pp. 4456-4461. |
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M.E.A. El-Mikkawy, T. Sogabe, “Notes on particular symmetric polynomials with applications”, Appl. Math. Comput., 215 (2010), pp. 3311-3317. |
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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. |
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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. |
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T. Sogabe, M.E.A. El-Mikkawy， “On a problem related to the Vandermonde determinant”, Discrete Appl. Math., 157 (2009), pp. 2997-2999. |
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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. |
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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. |
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T. Sogabe, T. Hoshi, S.-L. Zhang, 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. |
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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. |
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T. Sogabe, “New algorithms for solving periodic tridiagonal and periodic pentadiagonal linear systems”, Appl. Math. Comput., 202 (2008), pp. 850-856. |
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T. Sogabe, “A note on “A fast numerical algorithm for the determinant of a pentadiagonal matrix””, Appl. Math. Comput., 201 (2008), pp. 561-564. |
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T. Sogabe, “Numerical algorithms for solving comrade linear systems based on tridiagonal solvers”, Appl. Math. Comput., 198 (2008), pp. 117-122. |
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T. Sogabe, “A fast numerical algorithm for the determinant of a pentadiagonal matrix”, Appl. Math. Comput., 196 (2008), pp. 835-841. |
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T. Sogabe, “On a two-term recurrence for the determinant of a general matrix”, Appl. Math. Comput., 187 (2007), pp. 785-788. |
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T. Sogabe, S.-L. Zhang, “A COCR method for solving complex symmetric linear systems”, J. Comput. Appl. Math., 199 (2007), pp. 297-303. |
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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. |
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杉本振一郎，曽我部知広，張紹良，荻野正雄，武居周， “電磁界解析の複素対称行列向け積型反復法”， 電気学会論文誌, 145 (2025), pp. 87-97. |
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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． |
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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． |
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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． |
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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． |
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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． |
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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． |
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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． |
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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． |
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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． |
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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． |
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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． |
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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． |
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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． |
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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． |
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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． |
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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． |
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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. |
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S. Mizuno, Y. Moriizumi, T. S. Usuda, and 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. |
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L. Du, T. Sogabe and S.-L. Zhang “Quasi-minimal residual smoothing technique for the IDR(s) method”, JSIAM Letters, 3 (2011), pp. 13-16. |
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A. Imakura, T. Sogabe, and S.-L. Zhang, “A Modification of Implicit Wavelet Sparse Approximate Inverse Preconditioner Based on a Block Finger Pattern”, in: Frontiers of Computational Science 2008, eds. Y. Kaneda, M. Sasai, and K. Tachibana, Nagoya University, 2008, pp. 271-278. |
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T. Sogabe and S.-L. Zhang, (Invited Paper) “Numerical algorithms for solving shifted complex symmetric linear system”, in: Proceedings of the National Institute for Mathematical Sciences, Vol. 3, No. 9, (2008), pp. 145-158. |
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T. Sogabe, T. Hoshi, S.-L. Zhang, and T. Fujiwara On an application of the QMR_SYM method to complex symmetric shifted linear systems PAMM: Proc. Appl. Math. Mech. 7, (2007), pp. 2020081-2020082. |
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T. Sogabe, T. Hoshi, S.-L. Zhang, and 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. |
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T. Sogabe and 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, eds. Z.-C. Shi and H. Okamoto, Science Press, Beijing, 2006, pp. 120-130. |
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T. Sogabe and 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. |
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大橋あすか，曽我部知広， 「拡張テンソル和に対する最大・最小特異値計算 ～数値多重線形代数からのアプローチ～ 」， 京都大学数理解析研究所講究録1957，「新時代の科学技術を牽引する数値解析学」，2015.7， pp．38-44． |
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今倉暁， 曽我部知広，張紹良， 「シフト称線形方程式に対するリスタート付きShifted Krylov部分空間法について」， 京都大学数理解析研究所講究録1791，「科学技術計算における理論と応用の新展開」，2012.4， pp．47-56． |
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T. Miyata, T. Sogabe, and S.-L. Zhang, “On the convergence of the Jacobi-Davidson method based on a shift invariance property”， RIMS Kokyuroku 1733, Mathematical foundation and development of algorithms for scientific computing，2011.3, pp. 78-84. |
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T. Sogabe, T. Hoshi, S.-L. Zhang，and T. Fujiwara, “A fast numerical method for generalized shifted linear systems with complex symmetric matrices”， RIMS Kokyuroku 1719, Recent Developments of Numerical Analysis and Numerical Computation ALgorithms，2010.11, pp. 106-117. |
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T. Sogabe and S.-L. Zhang “CRS: a fast algorithm based on Bi-CR for solving nonsymmeric linear systems”, The First China-Japan-Korea Joint Conference on Numerical Mathematics & The Second East Asia SIAM Symposium, Hokkaido University Technical Report Series in Mathematics (北海道大学数学講究録), 112(2006), pp. 15-18. |
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木村欣司，平野照比古，荻田武史，山澤宏樹，曽我部知広，横山和弘， 「Real Root Countingに関する話題」， 京都大学数理解析研究所講究録1456，「CA-ALIAS」，2005.11，pp．180-187． |
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長谷川秀彦，曽我部知広，荻田 武史， 「非対称行列から生成された対称行列に対するCG 法」， 京都大学数理解析研究所講究録1362，「数値解析と新しい情報技術」， 2004.4， pp．6-12． |
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曽我部知広，張紹良， 「Bi-CR法の積型解法について」， 京都大学数理解析研究所講究録1362，「数値解析と新しい情報技術」，2004.4，pp．22-30． |
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曽我部知広，藤野清次，張紹良， 「COCG法の積型解法について」， 京都大学数理解析研究所講究録1320，「微分方程式の数値解法と線形計算」，2003.5，pp．201-211． |
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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. |
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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． |
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『20世紀のトップ10アルゴリズム』 （金田行雄・笹井理生 監修，張紹良 編），計算科学講座，共立出版，2022． 「3章：線形方程式のためのクリロフ部分空間法」 |
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『計算科学のための基本数理アルゴリズム』 （金田行雄・笹井理生 監修，張紹良 編），計算科学講座，共立出版，2019． 「2章：線形方程式」，「5章：非線形方程式」，「6章：関数近似」， 「8章：数値積分」， 「9章：常微分方程式」，「10章：偏微分方程式」 |
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（ハンドブック） 『応用数理ハンドブック』（薩摩順吉，大石進一，杉原正顯 編），朝倉書店，2013． 「連立1次方程式に対する直接解法」の項目，pp．408-411． 「連立1次方程式に対する反復解法」の項目，pp．412-415． |