Krylov Subspace Methods for Linear Systems —Principles of Algorithms
Spiringer Series in Computational Mathematics, Springer, 2023.
Series Editors: Randolph E. Bank, Wolfgang Hackbusch, Josef Stoer, and Harry Yserentant
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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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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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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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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. |
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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, and 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, and 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, and 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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L. Du, T. Sogabe, S.-L. Zhang, Quasi-minimal residual smoothing technique for the IDR(s) method, JSIAM Letters, 3 (2011), pp. 13-16. |
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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 and 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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T. Sogabe, T. Hoshi, S.-L. Zhang, T. Fujiwara, 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, S.-L. Zhang, 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. |
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T. Sogabe, S.-L. Zhang, 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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Krylov Subspace Methods for Linear Systems —Principles of Algorithms Spiringer Series in Computational Mathematics, Springer, 2023. Series Editors: Randolph E. Bank, Wolfgang Hackbusch, Josef Stoer, and Harry Yserentant |