List of publications




Journal Articles
Y. Miyatake and T. Sogabe,
“Adaptive projected SOR algorithms for nonnegative quadratic programming”,
Japan J. Ind. Appl. Math., (accepted)
F. Tatsuoka, T. Sogabe, T. Kemmochi, S.-L. Zhang,
Computing the matrix exponential with the double exponential formula,
Special Matrices (accepted)
Y. Satake, T. Sogabe, T. Kemmochi, S.-L. Zhang,
Matrix equation representation of the convolution equation and its unique solvability,
Special Matrices (accepted)
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.
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.
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.
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.
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.
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.
A. Ohashi, T. Sogabe,
Numerical algorithms for computing an arbitrary singular value of a tensor sum,
Axioms 10 (2021), 211. (14pp.)
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.
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.
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.
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)
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.
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.
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.
Y. Miyatake, T. Sogabe, S.-L. Zhang,
Adaptive SOR methods based on the Wolfe conditions,
Numer. Algorithms, 84 (2020), pp. 117-132.
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.
A. Ohashi, T. Sogabe
On computing the minimum singular value of a tensor sum,
Special Matrices, 7 (2019), pp. 95-106.
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.
S. Takahira, T. Sogabe, T. S. Usuda,
Bidiagonalization of (k, k + 1)-tridiagonal matrices,
Special Matrices, 7 (2019), pp. 20-26.
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.
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.
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.
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.
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.
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.
F. Yilmaz, T. Sogabe, E. Kirklar,
On the pfaffians and determinants of some skew-centrosymmetric matrices,
J. Integer Sequences, 20 (2017), pp. 1-9.
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.
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.
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.
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.
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.
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.
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.
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.
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, 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.
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.
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.
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.
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.
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.
J. Jia, T. Sogabe,
On particular solution of ordinary differential equations with constant coefficients,
Appl. Math. Comput., 219 (2013), pp. 6761-6767.
J. Jia, T. Sogabe,
A novel algorithm for solving quasi penta-diagonal linear systems,
J. Math. Chem., 51 (2013), pp. 881-889.
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.
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
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.
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.
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.
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.
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.
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.
T. Sogabe, M.E.A. El-Mikkawy,
Fast block diagonalization of k-tridiagonal matrices,
Appl. Math. Comput., 218 (2011), pp. 2740-2743.
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, 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.
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.
L. Du, T. Sogabe, S.-L. Zhang,
Quasi-minimal residual smoothing technique for the IDR(s) method,
JSIAM Letters, 3 (2011), pp. 13-16.
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.
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.
M.E.A. El-Mikkawy, T. Sogabe,
A new family of k-Fibonacci numbers,
Appl. Math. Comput. 215 (2010), pp. 4456-4461.
M.E.A. El-Mikkawy and T. Sogabe,
Notes on particular symmetric polynomials with applications,
Appl. Math. Comput., 215 (2010), pp. 3311-3317.
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.
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.E.A. El-Mikkawy,
On a problem related to the Vandermonde determinant,
Discrete Appl. Math., 157 (2009), pp. 2997-2999.
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.
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.
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.
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,
New algorithms for solving periodic tridiagonal and periodic pentadiagonal linear systems,
Appl. Math. Comput., 202 (2008), pp. 850-856.
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,
Numerical algorithms for solving comrade linear systems based on tridiagonal solvers,
Appl. Math. Comput., 198 (2008), pp. 117-122.
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.
T. Sogabe, S.-L. Zhang,
A COCR method for solving complex symmetric linear systems,
J. Comput. Appl. Math., 199 (2007), pp. 297-303.
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.



Book chapters
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.
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.
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.



Book

   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