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T. Hoshi, M. Kawamura, K. Yoshimi, Y. Motoyama, T. Misawa, Y. Yamaji, S. Todo, N. Kawashima, T. Sogabe,
gK -- Open-source library for the shifted Krylov subspace methodh,
Comput. Phys. Commun., (accepted)
K.-I. Ishikawa, T. Sogabe,
gA thick-restart Lanczos type method for Hermitian J-symmetric eigenvalue problemsh,
Japan J. Ind. Appl. Math., (accepted)
J. Jia, T. Sogabe,
gGeneralized Sherman-Morrison-Woodbury formula based algorithm for the inverses of opposite-bordered tridiagonal matricesh,
J. Math. Chem., (accepted)
T. Sogabe, A. Suzuki, S.-L. Zhang,
gAn implicit evaluation method of vector 2-norms arising from sphere constrained quadratic optimizationsh,
CSIAM Trans. Appl. Math., 1 (2020), pp. 142-154 (Invited)
S. Takahira, A. Ohashi, T. Sogabe, T. S. Usuda,
gQuantum algorithm for matrix functions by Cauchy's integral formulah,
Quantum Inform. Comput., 20:1-2 (2020), pp. 14-36.
Y. Satake, T. Sogabe, T. Kemmochi, S.-L. Zhang,
gOn a transformation of the *-congruence Sylvester equation for the least squares optimizationh,
Optim. Methods & Softw., (accepted)
F. Tatsuoka, T. Sogabe, Y. Miyatake, S.-L. Zhang,
gAlgorithms for the computation of the matrix logarithm based on the double exponential formulah,
J. Comput. Appl. Math., 373 (2020), (112396)
Y. Miyatake, T. Sogabe, S.-L. Zhang,
gAdaptive SOR methods based on the Wolfe conditionsh,
Numer. Algorithms, 84 (2020), pp. 117-132.
Y. Miyatake, T. Nakagawa, T. Sogabe, S.-L. Zhang,
gA structure-preserving Fourier pseudo-spectral linearly implicit scheme for the space-fractional nonlinear Schrödinger equationh,
J. Comput. Dyn., 6 (2019), pp. 361-383.
A. Ohashi, T. Sogabe,
gOn computing the minimum singular value of a tensor sumh,
Special Matrices, 7 (2019), pp. 95-106.
Y. Satake, M. Oozawa, T. Sogabe, Y. Miyatake, T. Kemmochi, S.-L. Zhang,
gRelation between the T-congruence Sylvester equation and the generalized Sylvester equationh,
Appl. Math. Lett., 96 (2019), pp. 7-13.
S. Takahira, T. Sogabe, T. S. Usuda,
gBidiagonalization of (k, k + 1)-tridiagonal matricesh,
Special Matrices, 7 (2019), pp. 20-26.
D. Lee, T. Hoshi, T. Sogabe, Y. Miyatake, S.-L. Zhang,
gSolution of the k-th eigenvalue problem in large-scale electronic structure calculationsh,
J. Comput. Phys., 371 (2018), pp. 618-632.
A. Imakura, T. Sogabe, S.-L. Zhang,
gA look-back-type restart for the restarted Krylov subspace methods for solving non-Hermitian linear systemsh,
Japan J. Ind. Appl. Math., 35 (2018), pp. 835-859.
Y. Miyatake, T. Sogabe, S.-L. Zhang,
gOn the equivalence between SOR-type methods for linear systems and the discrete gradient methods for gradient systemsh,
J. Comput. Appl. Math., 342 (2018), pp. 58-69.
K. Ooi, Y. Mizuno, T. Sogabe, Y. Yamamoto, S.-L. Zhang,
gSolution of a nonlinear eigenvalue problem using signed singular valuesh,
East Asia J. on Appl. Math., 7 (2018), pp. 799-809.
L. Du, T. Sogabe, S.-L. Zhang,
gA fast algorithm for solving tridiagonal quasi-Toeplitz linear systemsh,
Appl. Math. Lett., 75 (2018), pp. 74-81.
M. Oozawa, T. Sogabe, Y. Miyatake, S.-L. Zhang,
gOn a relationship between the T-congruence sylvester equation and the Lyapunov equationh,
J. Comput. Appl. Math., 329 (2018), pp. 51-56.
F. Yilmaz, T. Sogabe, E. Kirklar,
gOn the pfaffians and determinants of some skew-centrosymmetric matricesh,
J. Integer Sequences, 20 (2017), pp. 1-9.
Y. Miyatake, G. Eom, T. Sogabe, S.-L. Zhang,
gEnergy-preserving H1-Galerkin schemes for the Hunter-Saxton equationh,
J. Math. Res. Appl., 37 (2017), pp. 107-118.
F. Tatsuoka, T. Sogabe, Y. Miyatake, S.-L. Zhang
gA cost-efficient variant of the incremental Newton iteration for the matrix pth rooth,
J. Math. Res. Appl., 37 (2017), pp. 97-106.
A. Ohashi, T. Sogabe, T. S. Usuda,
gFast block diagonalization of (k, k')-pentadiagonal matricesh,
Int. J. Pure and Appl. Math., 106 (2016), pp. 513-523.
C. M. da Fonseca, T. Sogabe, F. Yilmaz,
gLower k-Hessenberg matrices and k-Fibonacci, Fibonacci-p and Pell (p,i) numbersh,
Gen. Math. Notes, 31 (2015), pp. 10-17.
A. Ohashi, T. Sogabe,
gOn computing maximum/minimum singular values of a generalized tensor sumh,
Electron. Trans. Numer. Anal., 43 (2015), pp. 244-254.
A. Ohashi, T. S. Usuda, T. Sogabe, F. Yilmaz,
gOn tensor product decomposition of k-tridiagonal Toeplitz matricesh,
Int. J. Pure and Appl. Math., 103 (2015), pp. 537-545.
A. Ohashi, T. Sogabe, T. S. Usuda,
gOn decomposition of k-tridiagonal l-Toeplitz matrices and its applicationsh,
Special Matrices, 3 (2015), pp. 200-206.
J. Jia, T. Sogabe, S. Li,
gA generalized symbolic Thomas algorithm for the solution of opposite-bordered tridiagonal linear systemsh,
J. Comput. Appl. Math., 290 (2015), pp. 423-432.
C. Wen, T.-Z. Huang, T. Sogabe,
gAn extension of two conjugate direction methods to Markov chain problemsh,
Computing and Informatics, 34 (2015), pp. 1001-1022.
L. Du, T. Sogabe, S.-L. Zhang,
gIDR(s) for solving shifted nonsymmetric linear systemsh,
J. Comput. Appl. Math., 274 (2015), pp. 35-43.
X.-M. Gu, T.-Z. Huang, L. Li, H.-B. Li, T Sogabe, M. Clemens,
gQuasi-minimal residual variants of the COCG and COCR methods for complex symmetric linear systems in electromagnetic simulationsh
IEEE Trans. Microw. Theory Techn., 62 (2014), pp. 2859-2867.
T. Sogabe, F. Yilmaz,
gA note on a fast breakdown-free algorithm for computing the determinants and the permanents of k-tridiagonal matricesh
Appl. Math. Comput., 249 (2014), pp. 98-102.
F. Yilmaz, T. Sogabe,
gA note on symmetric k-tridiagonal matrix family and the Fibonacci numbersh,
Int. J. Pure and Appl. Math., 96 (2014), pp. 289-298.
X.-M. Gu, T.-Z. Huang, J. Meng, T. Sogabe, H.-B. Li, L. Li,
gBiCR-type methods for families of shifted linear systemsh,
Comput. Math. Appl., 68 (2014), pp. 746-758.
L. Du, T. Sogabe, S.-L. Zhang,
gAn 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, S.-L. Zhang,
gAn interior eigenvalue problem from electronic structure calculationsh,
Japan J. Ind. Appl. Math., 30 (2013), pp. 625-633
J. Jia, T. Sogabe,
gOn particular solution of ordinary differential equations with constant coefficientsh,
Appl. Math. Comput., 219 (2013), pp. 6761-6767.
J. Jia, T. Sogabe,
gA novel algorithm for solving quasi penta-diagonal linear systemshC
J. Math. Chem., 51 (2013), pp. 881-889.
A. Imakura, T. Sogabe, S.-L. Zhang,
gAn efficient variant of the restarted shifted GMRES for solving shifted linear systemsh,
J. Math. Res. Appl., 33 (2013), pp. 127-141.
J. Jia, T. Sogabe, M.E.A. El-Mikkawy,
gInversion of k-tridiagonal matrices with Toeplitz structureh,
Comput. Math. Appl., 65 (2013), pp. 116-125
J. Jia, T. Sogabe,
gA novel algorithm and its parallelization for solving nearly penta-diagonal linear systemsh,
Int. J. Comput. Math., 90 (2013), pp. 435-444.
T. Sogabe, T. Hoshi, S.-L. Zhang, T. Fujiwara,@@@@@@@ @@@@
gSolution of generalized shifted linear systems with complex symmetric matricesh,
J. Comput. Phys., 231(2012), pp. 5669-5684.
J. Jia, Q. Kong, T. Sogabe,
gA fast numerical algorithm for solving nearly penta-diagonal linear systemsh,
Int. J. Comput. Math., 89 (2012), pp. 851-860.
T. Hoshi, S. Yamamoto, T. Fujiwara, T. Sogabe, S.-L. Zhang,
gAn order-N electronic structure theory with generalized eigen-value equations and its application to a ten-million-atom systemh,
J. Phys.: Condens. Matter, 24 (2012) 165502, pp. 1-5.
J. Jia, Q. Kong, T. Sogabe,
gA new algorithm for solving nearly penta-diagonal Toeplitz linear systemsh,
Comput. Math. Appl., 63 (2012), pp. 1238-1243.
A. Imakura, T. Sogabe, S.-L. ZhangC
gAn efficient variant of the GMRES(m) method based on error equationsh
East Asia J. on Appl. Math., 2 (2012), pp.19-32.
T. Sogabe, M.E.A. El-Mikkawy,
gFast block diagonalization of k-tridiagonal matricesh,
Appl. Math. Comput., 218 (2011), pp. 2740-2743.
L. Du, T. Sogabe, S.-L. Zhang,
gA variant of the IDR(s) method with quasi-minimal residual strategyh,
J. Comput. Appl. Math. 236 (2011), pp. 621-630.
L. Du, T. Sogabe, B. Yu, Y. Yamamoto, S.-L. Zhang,
gA block IDR(s) method for nonsymmetric linear systems with multiple right-hand sidesh,
J. Comput. Appl. Math., 235 (2011), pp. 4095-4106.
H. Teng, T. Fujiwara, T. Hoshi, T. Sogabe, S.-L. Zhang, S. Yamamoto,
gEfficient and accurate linear algebraic methods for large-scale electronic structure calculations with non-orthogonal atomic orbitalsh,
Phys. Rev. B 83, 165103 (2011), pp. 1-12.
T. Sogabe, S.-L. Zhang,@@@@@@@ @@@@@@
gAn extension of the COCR method to solving shifted linear systems with complex symmetric matricesh,
East Asia J. on Appl. Math., 1 (2011), pp. 97-107.
Y. Mizuno, K. Ohi, T. Sogabe, Y. Yamamoto, Y. Kaneda,@@@@@@@
gFour-point correlation function of a passive scalar field in rapidly fluctuating turbulence: Numerical analysis of an exact closure equation h,
Phys. Rev. E 82, 036316 (2010), pp.1-9.
M.E.A. El-Mikkawy, T. Sogabe,
gA new family of k-Fibonacci numbersh,
Appl. Math. Comput. 215 (2010), pp. 4456-4461.
M.E.A. El-Mikkawy, T. Sogabe,
gNotes on particular symmetric polynomials with applicationsh,
Appl. Math. Comput., 215 (2010), pp. 3311-3317.
T. Fujiwara, T. Hoshi, S. Yamamoto, T. Sogabe, S.-L. Zhang, @@@@ @
gA novel algorithm of large-scale simultaneous linear equationsh,
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, @@@@@@@
gLanczos-type variants of the COCR method for complex nonsymmetric linear systemsh,
J. Comput. Phys., 228 (2009), pp. 6376-6394.
T. Sogabe, M.E.A. El-MikkawyC @@@@@@@ @@@@
gOn a problem related to the Vandermonde determinanth,
Discrete Appl. Math., 157 (2009), pp. 2997-2999.
A. Imakura, T. Sogabe, S.-L. ZhangC @@@@@@@ @
gAn implicit wavelet sparse approximate inverse preconditioner using block finger patternh,
Numer. Linear Algebra. Appl., 16 (2009), pp.915-928.
T. Sogabe, M. Sugihara, S.-L. Zhang, @@@@@@@@@@@@@@@@
gAn extension of the conjugate residual method to nonsymmetric linear systemsh,
J. Comput. Appl. Math., 226 (2009), pp. 103-113.
T. Sogabe, T. Hoshi, S.-L. Zhang, T. Fujiwara, @@@@@@
gOn a weighted quasi-residual minimization strategy for solving complex symmetric shifted linear systemsh,
Electron. Trans. Numer. Anal., 31 (2008), pp. 126-140.
S. Yamamoto, T. Sogabe, T. Hoshi, S.-L. Zhang, T. Fujiwara, @
gShifted COCG method and its application to double orbital extended Hubbard modelh,
J. Phys. Soc. Jpn., Vol. 77, No. 11, 114713 (2008), pp. 1-8. @@@@@
T. Sogabe, @@@@@@@@@@@@@@@@
gNew algorithms for solving periodic tridiagonal and periodic pentadiagonal linear systemsh,
Appl. Math. Comput., 202 (2008), pp. 850-856.
T. Sogabe,@@@@@@@ @@@@@@
gA note on gA fast numerical algorithm for the determinant of a pentadiagonal matrixhh,
Appl. Math. Comput., 201 (2008), pp. 561-564.
T. Sogabe,@@@@@@@ @@@@@@
gNumerical algorithms for solving comrade linear systems based on tridiagonal solversh,
Appl. Math. Comput., 198 (2008), pp. 117-122.
T. Sogabe,@@@@@@@ @@@@@@
gA fast numerical algorithm for the determinant of a pentadiagonal matrixh,
Appl. Math. Comput., 196 (2008), pp. 835-841.
T. Sogabe,@@
gOn a two-term recurrence for the determinant of a general matrixh,
Appl. Math. Comput., 187 (2007), pp. 785-788.
T. Sogabe, S.-L. Zhang,
gA COCR method for solving complex symmetric linear systemsh,
J. Comput. Appl. Math., 199 (2007), pp. 297-303.
R. Takayama, T. Hoshi, T. Sogabe, S.-L. Zhang, T. Fujiwara,@@
gLinear algebraic calculation of Green's function for large-scale electronic structure theoryh,
Phys. Rev. B 73, 165108 (2006), pp. 1-9.


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K. Nakano, T. Kemmochi, Y. Miyatake, T. Sogabe, S.-L. Zhang,
gModified Strang splitting for semilinear parabolic problemsh,
JSIAM Letters, 11 (2019), pp. 77-80.
S. Mizuno, Y. Moriizumi, T. S. Usuda, and T. Sogabe,
gAn initial guess of Newton's method for the matrix square root based on a sphere constrained optimization problemh,
JSIAM Letters, 8 (2016), pp. 17-20.
L. Du, T. Sogabe and S.-L. Zhang
gQuasi-minimal residual smoothing technique for the IDR(s) methodh,
JSIAM Letters, 3 (2011), pp. 13-16.



Proceedings (Refereed)
A. Imakura, T. Sogabe, and S.-L. Zhang,
gA Modification of Implicit Wavelet Sparse Approximate Inverse Preconditioner Based on a Block Finger Patternh,
in: Frontiers of Computational Science 2008, eds. Y. Kaneda, M. Sasai, and K. Tachibana, Nagoya University, 2008, pp. 271-278.
T. Sogabe and S.-L. Zhang, (Invited Paper)
gNumerical algorithms for solving shifted complex symmetric linear systemh,
in: Proceedings of the National Institute for Mathematical Sciences, Vol. 3, No. 9, (2008), pp. 145-158.
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.
T. Sogabe, T. Hoshi, S.-L. Zhang, and T. Fujiwara, (Invited Paper)
gA numerical method for calculating the Green's function arising from electronic structure theoryh,
in: Frontiers of Computational Science, eds. Y. Kaneda, H. Kawamura and M. Sasai,
Springer-Verlag, Berlin/Heidelberg, 2007, pp. 189-195.
T. Sogabe and S.-L. Zhang, (Invited Paper)
gAn iterative method based on an A-biorthogonalization process for nonsymmetric linear systemsh,
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.
T. Sogabe and S.-L. Zhang, (Invited Lecture)
gExtended conjugate residual methods for solving nonsymmetric linear systemsh,
in: Numerical Linear Algebra and Optimization, ed. Y. Yuan, Science Press, Beijing/NewYork, 2004, pp. 88-99.



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RIMS Kokyuroku 1733, Mathematical foundation and development of algorithms for scientific computingC2011.3, pp. 78-84.
T. Sogabe, T. Hoshi, S.-L. ZhangCand T. Fujiwara,
gA fast numerical method for generalized shifted linear systems with complex symmetric matriceshC
RIMS Kokyuroku 1719, Recent Developments of Numerical Analysis and Numerical Computation ALgorithmsC2010.11, pp. 106-117.
T. Sogabe and S.-L. ZhangC
gOn the use of the QMR SYM method for solving complex symmetric shifted linear systemshC
RIMS Kokyuroku 1614, High Performance Algorithms for Computational Science and Their ApplicationsC2008.10, pp. 124-135.
T. Sogabe and S.-L. Zhang
gCRS: a fast algorithm based on Bi-CR for solving nonsymmeric linear systemsh,
The First China-Japan-Korea Joint Conference on Numerical Mathematics & The Second East Asia SIAM Symposium,
Hokkaido University Technical Report Series in Mathematics (kCwwu^), 112(2006), pp. 15-18.
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