Schwartz, Oded; Vaknin, Noa Pebbling game and alternative basis for high performance matrix multiplication. (English) Zbl 1527.15001 SIAM J. Sci. Comput. 45, No. 6, C277-C303 (2023). MSC: 15-04 65F99 65K05 PDFBibTeX XMLCite \textit{O. Schwartz} and \textit{N. Vaknin}, SIAM J. Sci. Comput. 45, No. 6, C277--C303 (2023; Zbl 1527.15001) Full Text: DOI
Lin, Lin; Wu, Xiaojie Numerical solution of large scale Hartree-Fock-Bogoliubov equations. (English) Zbl 1520.65077 ESAIM, Math. Model. Numer. Anal. 55, No. 3, 763-787 (2021). Reviewer: Zhiming Chen (Beijing) MSC: 65N25 65F15 15A18 60H10 82D55 81V74 35Q40 PDFBibTeX XMLCite \textit{L. Lin} and \textit{X. Wu}, ESAIM, Math. Model. Numer. Anal. 55, No. 3, 763--787 (2021; Zbl 1520.65077) Full Text: DOI arXiv
Ming, Liangjie; Zhang, Yunong; Guo, Jinjin; Liu, Xiao; Li, Zhonghua New models for solving time-varying LU decomposition by using ZNN method and ZeaD formulas. (English) Zbl 1477.65057 J. Math. 2021, Article ID 6627298, 13 p. (2021). MSC: 65F05 15A23 PDFBibTeX XMLCite \textit{L. Ming} et al., J. Math. 2021, Article ID 6627298, 13 p. (2021; Zbl 1477.65057) Full Text: DOI
Keyes, D. E.; Ltaief, H.; Turkiyyah, G. Hierarchical algorithms on hierarchical architectures. (English) Zbl 1462.65048 Philos. Trans. R. Soc. Lond., A, Math. Phys. Eng. Sci. 378, No. 2166, Article ID 20190055, 16 p. (2020). MSC: 65F99 15A23 PDFBibTeX XMLCite \textit{D. E. Keyes} et al., Philos. Trans. R. Soc. Lond., A, Math. Phys. Eng. Sci. 378, No. 2166, Article ID 20190055, 16 p. (2020; Zbl 1462.65048) Full Text: DOI
Mohanty, Sraban Kumar; Sajith, G. An input/output efficient algorithm for Hessenberg reduction. (English) Zbl 1480.65110 Int. J. Found. Comput. Sci. 30, No. 8, 1279-1300 (2019). MSC: 65F99 68W40 15A23 PDFBibTeX XMLCite \textit{S. K. Mohanty} and \textit{G. Sajith}, Int. J. Found. Comput. Sci. 30, No. 8, 1279--1300 (2019; Zbl 1480.65110) Full Text: DOI
Amestoy, Patrick R.; de la Kethulle de Ryhove, Sébastien; L’Excellent, Jean-Yves; Moreau, Gilles; Shantsev, Daniil V. Efficient use of sparsity by direct solvers applied to 3D controlled-source EM problems. (English) Zbl 1427.65033 Comput. Geosci. 23, No. 6, 1237-1258 (2019). MSC: 65F05 15A23 65F50 65Y05 86A20 86A22 PDFBibTeX XMLCite \textit{P. R. Amestoy} et al., Comput. Geosci. 23, No. 6, 1237--1258 (2019; Zbl 1427.65033) Full Text: DOI Link
Dawson, William; Nakajima, Takahito Massively parallel sparse matrix function calculations with NTPoly. (English) Zbl 1524.65192 Comput. Phys. Commun. 225, 154-165 (2018). MSC: 65F50 15-04 65Y05 65Y15 PDFBibTeX XMLCite \textit{W. Dawson} and \textit{T. Nakajima}, Comput. Phys. Commun. 225, 154--165 (2018; Zbl 1524.65192) Full Text: DOI
Dongarra, Jack; Gates, Mark; Haidar, Azzam; Kurzak, Jakub; Luszczek, Piotr; Tomov, Stanimire; Yamazaki, Ichitaro The singular value decomposition: anatomy of optimizing an algorithm for extreme scale. (English) Zbl 1410.65114 SIAM Rev. 60, No. 4, 808-865 (2018). Reviewer: Wei-Ru Xu (Chengdu) MSC: 65F15 65Y15 15A18 15A23 65Y05 PDFBibTeX XMLCite \textit{J. Dongarra} et al., SIAM Rev. 60, No. 4, 808--865 (2018; Zbl 1410.65114) Full Text: DOI
Kalantzis, Vassilis; Xi, Yuanzhe; Saad, Yousef Beyond automated multilevel substructuring: domain decomposition with rational filtering. (English) Zbl 1394.65030 SIAM J. Sci. Comput. 40, No. 4, C477-C502 (2018). MSC: 65F15 15A18 65F50 65Y05 PDFBibTeX XMLCite \textit{V. Kalantzis} et al., SIAM J. Sci. Comput. 40, No. 4, C477--C502 (2018; Zbl 1394.65030) Full Text: DOI arXiv
Adlerborn, Björn; Karlsson, Lars; Kågström, Bo Distributed one-stage Hessenberg-triangular reduction with wavefront scheduling. (English) Zbl 1382.65095 SIAM J. Sci. Comput. 40, No. 2, C157-C180 (2018). MSC: 65F15 15A18 PDFBibTeX XMLCite \textit{B. Adlerborn} et al., SIAM J. Sci. Comput. 40, No. 2, C157--C180 (2018; Zbl 1382.65095) Full Text: DOI
Gentle, James E. Matrix algebra. Theory, computations and applications in statistics. 2nd edition. (English) Zbl 1386.15002 Springer Texts in Statistics. Cham: Springer (ISBN 978-3-319-64866-8/pbk; 978-3-319-64867-5/ebook). xxix, 648 p. (2017). Reviewer: Frank Uhlig (Auburn) MSC: 15-01 62-01 65-01 PDFBibTeX XMLCite \textit{J. E. Gentle}, Matrix algebra. Theory, computations and applications in statistics. 2nd edition. Cham: Springer (2017; Zbl 1386.15002) Full Text: DOI
Xin, Zixing; Xia, Jianlin; de Hoop, Maarten V.; Cauley, Stephen; Balakrishnan, Venkataramanan A distributed-memory randomized structured multifrontal method for sparse direct solutions. (English) Zbl 1393.65002 SIAM J. Sci. Comput. 39, No. 4, C292-C318 (2017). MSC: 65F50 15A23 65F05 65F30 65Y05 65Y10 65Y20 PDFBibTeX XMLCite \textit{Z. Xin} et al., SIAM J. Sci. Comput. 39, No. 4, C292--C318 (2017; Zbl 1393.65002) Full Text: DOI
Wen, Zaiwen; Yang, Chao; Liu, Xin; Zhang, Yin Trace-penalty minimization for large-scale eigenspace computation. (English) Zbl 1373.65026 J. Sci. Comput. 66, No. 3, 1175-1203 (2016). Reviewer: Adhemar Bultheel (Leuven) MSC: 65F15 65K05 90C06 15A22 65Y20 PDFBibTeX XMLCite \textit{Z. Wen} et al., J. Sci. Comput. 66, No. 3, 1175--1203 (2016; Zbl 1373.65026) Full Text: DOI Link
Drmač, Zlatko; Gugercin, Serkan A new selection operator for the discrete empirical interpolation method – improved a priori error bound and extensions. (English) Zbl 1382.65193 SIAM J. Sci. Comput. 38, No. 2, A631-A648 (2016). MSC: 65L05 15A12 15A23 93B11 93B40 PDFBibTeX XMLCite \textit{Z. Drmač} and \textit{S. Gugercin}, SIAM J. Sci. Comput. 38, No. 2, A631--A648 (2016; Zbl 1382.65193) Full Text: DOI arXiv
Vecharynski, Eugene; Yang, Chao; Pask, John E. A projected preconditioned conjugate gradient algorithm for computing many extreme eigenpairs of a Hermitian matrix. (English) Zbl 1349.65133 J. Comput. Phys. 290, 73-89 (2015). MSC: 65F15 65F08 15B57 PDFBibTeX XMLCite \textit{E. Vecharynski} et al., J. Comput. Phys. 290, 73--89 (2015; Zbl 1349.65133) Full Text: DOI arXiv
Willems, Paul R.; Lang, Bruno A framework for the \(\text{MR}^3\) algorithm: theory and implementation. (English) Zbl 1266.65061 SIAM J. Sci. Comput. 35, No. 2, A740-A766 (2013). MSC: 65F15 65G50 15A18 PDFBibTeX XMLCite \textit{P. R. Willems} and \textit{B. Lang}, SIAM J. Sci. Comput. 35, No. 2, A740--A766 (2013; Zbl 1266.65061) Full Text: DOI
Schauer, Marco; Roman, Jose E.; Quintana-Ortí, Enrique S.; Langer, Sabine Parallel computation of 3-D soil-structure interaction in time domain with a coupled FEM/SBFEM approach. (English) Zbl 1311.74077 J. Sci. Comput. 52, No. 2, 446-467 (2012). MSC: 74L10 74S05 65L60 15A24 PDFBibTeX XMLCite \textit{M. Schauer} et al., J. Sci. Comput. 52, No. 2, 446--467 (2012; Zbl 1311.74077) Full Text: DOI Link
Demmel, James; Grigori, Laura; Hoemmen, Mark; Langou, Julien Communication-optimal parallel and sequential QR and LU factorizations. (English) Zbl 1241.65028 SIAM J. Sci. Comput. 34, No. 1, A206-A239 (2012). MSC: 65F05 65Y05 65Y20 15A23 65F25 65F20 PDFBibTeX XMLCite \textit{J. Demmel} et al., SIAM J. Sci. Comput. 34, No. 1, A206--A239 (2012; Zbl 1241.65028) Full Text: DOI arXiv
Vömel, Christof; Parlett, Beresford N. Detecting localization in an invariant subspace. (English) Zbl 1232.15011 SIAM J. Sci. Comput. 33, No. 6, 3447-3467 (2011). MSC: 15A18 15A23 PDFBibTeX XMLCite \textit{C. Vömel} and \textit{B. N. Parlett}, SIAM J. Sci. Comput. 33, No. 6, 3447--3467 (2011; Zbl 1232.15011) Full Text: DOI
Kourniotis, M.; Mitrouli, M.; Triantafyllou, D. Parallel QR processing of generalized Sylvester matrices. (English) Zbl 1211.65036 Theor. Comput. Sci. 412, No. 16, 1484-1491 (2011). MSC: 65F05 15A23 65Y05 PDFBibTeX XMLCite \textit{M. Kourniotis} et al., Theor. Comput. Sci. 412, No. 16, 1484--1491 (2011; Zbl 1211.65036) Full Text: DOI
Agullo, Emmanuel; Bouwmeester, Henricus; Dongarra, Jack; Kurzak, Jakub; Langou, Julien; Rosenberg, Lee Towards an efficient tile matrix inversion of symmetric positive definite matrices on multicore architectures. (English) Zbl 1323.65022 Palma, José M. Laginha M. (ed.) et al., High performance computing for computational science – VECPAR 2010. 9th international conference, Berkeley, CA, USA, June 22–25, 2010. Revised selected papers. Berlin: Springer (ISBN 978-3-642-19327-9/pbk). Lecture Notes in Computer Science 6449, 129-138 (2011). MSC: 65F05 65Y05 65Y10 15A09 PDFBibTeX XMLCite \textit{E. Agullo} et al., Lect. Notes Comput. Sci. 6449, 129--138 (2011; Zbl 1323.65022) Full Text: DOI
Baboulin, Marc; Dongarra, Jack; Gratton, Serge; Langou, Julien Computing the conditioning of the components of a linear least-squares solution. (English) Zbl 1224.65104 Numer. Linear Algebra Appl. 16, No. 7, 517-533 (2009). MSC: 65F20 62J05 15A12 65J10 85A15 86A30 PDFBibTeX XMLCite \textit{M. Baboulin} et al., Numer. Linear Algebra Appl. 16, No. 7, 517--533 (2009; Zbl 1224.65104) Full Text: DOI arXiv Link
Defez, Emilio; Sastre, Jorge; Ibáñez, Javier; Ruiz, Pedro A. Computing matrix functions solving coupled differential models. (English) Zbl 1185.65078 Math. Comput. Modelling 50, No. 5-6, 831-839 (2009). MSC: 65F60 15A16 PDFBibTeX XMLCite \textit{E. Defez} et al., Math. Comput. Modelling 50, No. 5--6, 831--839 (2009; Zbl 1185.65078) Full Text: DOI
Vidal, Antonio M.; Garcia, Victor M.; Alonso, Pedro; Bernabeu, Miguel O. Parallel computation of the eigenvalues of symmetric Toeplitz matrices through iterative methods. (English) Zbl 1243.65044 J. Parallel Distrib. Comput. 68, No. 8, 1113-1121 (2008). MSC: 65F15 15B05 65Y05 65F10 PDFBibTeX XMLCite \textit{A. M. Vidal} et al., J. Parallel Distrib. Comput. 68, No. 8, 1113--1121 (2008; Zbl 1243.65044) Full Text: DOI
Bosner, Nela; Barlow, Jesse L. Block and parallel versions of one-sided bidiagonalization. (English) Zbl 1149.65031 SIAM J. Matrix Anal. Appl. 29, No. 3, 927-953 (2007). Reviewer: Liu Xinguo (Qingdao) MSC: 65F30 15A18 68W10 PDFBibTeX XMLCite \textit{N. Bosner} and \textit{J. L. Barlow}, SIAM J. Matrix Anal. Appl. 29, No. 3, 927--953 (2007; Zbl 1149.65031) Full Text: DOI
Campos, Carlos; Guerrero, David; Hernández, Vicente; Ralha, Rui Parallel bidiagonalization of a dense matrix. (English) Zbl 1145.65028 SIAM J. Matrix Anal. Appl. 29, No. 3, 826-837 (2007). MSC: 65F30 65Y05 15A21 PDFBibTeX XMLCite \textit{C. Campos} et al., SIAM J. Matrix Anal. Appl. 29, No. 3, 826--837 (2007; Zbl 1145.65028) Full Text: DOI
Barrachina, Sergio; Benner, Peter; Quintana-Ortí, Enrique S. Efficient algorithms for generalized algebraic Bernoulli equations based on the matrix sign function. (English) Zbl 1132.65033 Numer. Algorithms 46, No. 4, 351-368 (2007). MSC: 65F30 15A24 65Y05 93C05 93D15 PDFBibTeX XMLCite \textit{S. Barrachina} et al., Numer. Algorithms 46, No. 4, 351--368 (2007; Zbl 1132.65033) Full Text: DOI
Benner, Peter; Quintana-Ortí, Enrique S.; Quintana-Ortí, Gregorio Solving stable Sylvester equations via rational iterative schemes. (English) Zbl 1098.65041 J. Sci. Comput. 28, No. 1, 51-83 (2006). MSC: 65F30 15A24 65Y05 PDFBibTeX XMLCite \textit{P. Benner} et al., J. Sci. Comput. 28, No. 1, 51--83 (2006; Zbl 1098.65041) Full Text: DOI
Benner, Peter; Byers, Ralph An arithmetic for matrix pencils: theory and new algorithms. (English) Zbl 1101.65046 Numer. Math. 103, No. 4, 539-573 (2006). Reviewer: Liu Xinguo (Qingdao) MSC: 65F30 15A22 PDFBibTeX XMLCite \textit{P. Benner} and \textit{R. Byers}, Numer. Math. 103, No. 4, 539--573 (2006; Zbl 1101.65046) Full Text: DOI Link
Costa, Cecília; Azevedo Perdicoúlis, T.-P.; Serôdio, R. A study on quaternion block quasi-tridiagonal systems. (English) Zbl 1090.15003 Comput. Math. Appl. 50, No. 7, 1011-1016 (2005). Reviewer: Hans Havlicek (Wien) MSC: 15A06 15B33 65F05 PDFBibTeX XMLCite \textit{C. Costa} et al., Comput. Math. Appl. 50, No. 7, 1011--1016 (2005; Zbl 1090.15003) Full Text: DOI
Bartlett, Roscoe A.; van Bloemen Waanders, Bart G.; Heroux, Michael A. Vector reduction/transformation operators. (English) Zbl 1072.65059 ACM Trans. Math. Softw. 30, No. 1, 62-85 (2004). MSC: 65F30 15A04 PDFBibTeX XMLCite \textit{R. A. Bartlett} et al., ACM Trans. Math. Softw. 30, No. 1, 62--85 (2004; Zbl 1072.65059) Full Text: DOI
Cao, Yang; Petzold, Linda A subspace error estimate for linear systems. (English) Zbl 1036.65042 SIAM J. Matrix Anal. Appl. 24, No. 3, 787-801 (2003). MSC: 65F35 15A12 PDFBibTeX XMLCite \textit{Y. Cao} and \textit{L. Petzold}, SIAM J. Matrix Anal. Appl. 24, No. 3, 787--801 (2003; Zbl 1036.65042) Full Text: DOI
Li, Xiaoye S.; Martin, Michael C.; Thompson, Brandon J.; Tung, Teresa; Yoo, Daniel J.; Demmel, James W.; Bailey, David H.; Henry, Greg; Hida, Yozo; Iskandar, Jimmy; Kahan, William; Kang, Suh Y.; Kapur, Anil Design, implementation and testing of extended and mixed precision BLAS. (English) Zbl 1070.65523 ACM Trans. Math. Softw. 28, No. 2, 1512-205 (2002). MSC: 65Fxx 15-04 65Y20 PDFBibTeX XMLCite \textit{X. S. Li} et al., ACM Trans. Math. Softw. 28, No. 2, 1512--205 (2002; Zbl 1070.65523) Full Text: DOI Link
Benner, Peter; Quintana-Ortí, Enrique S.; Quintana-Ortí, Gregorio Numerical solution of discrete stable linear matrix equations on multicomputers. (English) Zbl 1009.65039 Parallel Algorithms Appl. 17, No. 2, 127-146 (2002). MSC: 65K10 15A24 93C55 94A08 65F30 93E11 65Y05 65Y20 PDFBibTeX XMLCite \textit{P. Benner} et al., Parallel Algorithms Appl. 17, No. 2, 127--146 (2002; Zbl 1009.65039) Full Text: DOI
Beaumont, Olivier; Boudet, Vincent; Petitet, Antoine; Rastello, Fabrice; Robert, Yves A proposal for a heterogeneous cluster ScaLAPACK (dense linear solvers). (English) Zbl 1315.65113 IEEE Trans. Comput. 50, No. 10, 1052-1070 (2001). MSC: 65Y05 15-04 PDFBibTeX XMLCite \textit{O. Beaumont} et al., IEEE Trans. Comput. 50, No. 10, 1052--1070 (2001; Zbl 1315.65113) Full Text: DOI Link
Benner, Peter; Byers, Ralph Evaluating products of matrix pencils and collapsing matrix products. (English) Zbl 1055.65053 Numer. Linear Algebra Appl. 8, No. 6-7, 357-380 (2001). MSC: 65F30 93C55 65K10 65G50 15A22 PDFBibTeX XMLCite \textit{P. Benner} and \textit{R. Byers}, Numer. Linear Algebra Appl. 8, No. 6--7, 357--380 (2001; Zbl 1055.65053) Full Text: DOI
Quintana-Ortí, Enrique S.; van de Geijn, Robert Specialized parallel algorithms for solving Lyapunov and Stein equations. (English) Zbl 0997.65070 J. Parallel Distrib. Comput. 61, No. 10, 1489-1504 (2001). MSC: 65F30 65Y15 15A24 PDFBibTeX XMLCite \textit{E. S. Quintana-Ortí} and \textit{R. van de Geijn}, J. Parallel Distrib. Comput. 61, No. 10, 1489--1504 (2001; Zbl 0997.65070) Full Text: DOI Link
Benner, P.; Byers, R.; Quintana-Ortí, E. S.; Quintana-Ortí, G. Solving algebraic Riccati equations on parallel computers using Newton’s method with exact line search. (English) Zbl 0949.65041 Parallel Comput. 26, No. 10, 1345-1368 (2000). MSC: 65F30 15A24 65Y05 PDFBibTeX XMLCite \textit{P. Benner} et al., Parallel Comput. 26, No. 10, 1345--1368 (2000; Zbl 0949.65041) Full Text: DOI
Östermark, Ralf A flexible multicomputer algorithm for elementary matrix operations. (English) Zbl 0947.65046 Comput. Oper. Res. 27, No. 3, 245-268 (2000). MSC: 65F30 15-04 65Y20 65F50 65Y05 65K05 90C30 PDFBibTeX XMLCite \textit{R. Östermark}, Comput. Oper. Res. 27, No. 3, 245--268 (2000; Zbl 0947.65046) Full Text: DOI
Dackland, Krister; Kågström, Bo Blocked algorithms and software for reduction of a regular matrix pair to generalized Schur form. (English) Zbl 0962.65041 ACM Trans. Math. Softw. 25, No. 4, 425-454 (1999). MSC: 65F30 15A21 65F15 PDFBibTeX XMLCite \textit{K. Dackland} and \textit{B. Kågström}, ACM Trans. Math. Softw. 25, No. 4, 425--454 (1999; Zbl 0962.65041) Full Text: DOI
Dongarra, Jack J.; Walker, David W. Constructing linear algebra software libraries for high-performance computers. (English) Zbl 0938.65057 Chan, Raymond H. (ed.) et al., Iterative methods in scientific computing. Papers from the winter school on Iterative methods in scientific computing and their applications held in Hong Kong, December 14-20, 1995. Singapore: Springer. 111-167 (1997). MSC: 65Fxx 15-04 65Y15 PDFBibTeX XMLCite \textit{J. J. Dongarra} and \textit{D. W. Walker}, in: Iterative methods in scientific computing. Papers from the winter school on Iterative methods in scientific computing and their applications held in Hong Kong, December 14--20, 1995. Singapore: Springer. 111--167 (1997; Zbl 0938.65057)
Blackford, L. S.; Choi, J.; Cleary, A.; D’Azevedo, E.; Demmel, J.; Dhillon, I.; Dongarra, J.; Hammarling, S.; Henry, G.; Petitet, A.; Stanley, K.; Walker, D.; Whaley, R. C. ScaLAPACK users’ guide. Incl. 1 CD-ROM. (English) Zbl 0886.65022 Software - Environments - Tools, 4. Philadelphia, PA: SIAM, Society for Industrial and Applied Mathematics. 325 p. (1997). MSC: 65Fxx 15-04 65Y15 65Y05 PDFBibTeX XMLCite \textit{L. S. Blackford} et al., ScaLAPACK users' guide. Incl. 1 CD-ROM. Philadelphia, PA: SIAM (1997; Zbl 0886.65022) Full Text: DOI
Choi, Jaeyoung; Dongarra, Jack J.; Walker, David W. The design of a parallel dense linear algebra software library: Reduction to Hessenberg, tridiagonal, and bidiagonal form. (English) Zbl 0839.65050 Numer. Algorithms 10, No. 3-4, 379-399 (1995). Reviewer: N.Köckler (Paderborn) MSC: 65F30 65F15 15A21 15A12 65Y15 65Y20 65F35 PDFBibTeX XMLCite \textit{J. Choi} et al., Numer. Algorithms 10, No. 3--4, 379--399 (1995; Zbl 0839.65050) Full Text: DOI