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[1] James Demmel,et al. The generalized Schur decomposition of an arbitrary pencil A–λB—robust software with error bounds and applications. Part II: software and applications , 1993, TOMS.
[2] V. Kublanovskaya,et al. An approach to solving the spectral problem of A-λB , 1983 .
[3] A. Malyshev. Computing invariant subspaces of a regular linear pencil of matrices , 1989 .
[4] D. Sorensen,et al. LAPACK Working Note No. 2: Block reduction of matrices to condensed forms for eigenvalue computations , 1987 .
[5] Ya Yan Lu,et al. Eigenvalues of the Laplacian through boundary integral equations , 1991 .
[6] James Demmel,et al. Minimizing Communication in Numerical Linear Algebra , 2009, SIAM J. Matrix Anal. Appl..
[7] Ed Anderson,et al. LAPACK users' guide - [release 1.0] , 1992 .
[8] James Demmel,et al. Communication avoiding successive band reduction , 2012, PPoPP '12.
[9] H. Rutishauser. On jacobi rotation patterns , 1963 .
[10] Greg Henry. The Shifted Hessenberg System Solve Computation , 1994 .
[11] Dror Irony,et al. Communication lower bounds for distributed-memory matrix multiplication , 2004, J. Parallel Distributed Comput..
[12] S. Godunov,et al. Circular dichotomy of the spectrum of a matrix , 1988 .
[13] H. T. Kung,et al. I/O complexity: The red-blue pebble game , 1981, STOC '81.
[14] J. L. Howland. The sign matrix and the separation of matrix eigenvalues , 1983 .
[15] G. Stewart. On graded QR decompositions of products of matrices , 1994 .
[16] Jack Dongarra,et al. ScaLAPACK Users' Guide , 1987 .
[17] James Demmel,et al. Fast linear algebra is stable , 2006, Numerische Mathematik.
[18] Matemática,et al. Society for Industrial and Applied Mathematics , 2010 .
[19] L. Trefethen,et al. Eigenvalues and pseudo-eigenvalues of Toeplitz matrices , 1992 .
[20] Xiaobai Sun,et al. Parallel tridiagonalization through two-step band reduction , 1994, Proceedings of IEEE Scalable High Performance Computing Conference.
[21] James Demmel,et al. Communication-optimal Parallel and Sequential QR and LU Factorizations , 2008, SIAM J. Sci. Comput..
[22] Alan Edelman,et al. The dimension of matrices (matrix pencils) with given Jordan (Kronecker) canonical forms , 1995 .
[23] L. Auslander,et al. On parallelizable eigensolvers , 1992 .
[24] James Demmel,et al. The generalized Schur decomposition of an arbitrary pencil A–λB—robust software with error bounds and applications. Part I: theory and algorithms , 1993, TOMS.
[25] Marc Snir,et al. GETTING UP TO SPEED THE FUTURE OF SUPERCOMPUTING , 2004 .
[26] A. Malyshev. Parallel Algorithm for Solving Some Spectral Problems of Linear Algebra , 1993 .
[27] G. Stewart. Gershgorin theory for the generalized eigenvalue problem , 1975 .
[28] J. Demmel,et al. An inverse free parallel spectral divide and conquer algorithm for nonsymmetric eigenproblems , 1997 .
[29] Per Christian Hansen,et al. Some Applications of the Rank Revealing QR Factorization , 1992, SIAM J. Sci. Comput..
[30] C. Bischof. Incremental condition estimation , 1990 .
[31] Christian H. Bischof,et al. A framework for symmetric band reduction , 2000, TOMS.
[32] Enrique S. Quintana-Ortí,et al. Specialized Spectral Division Algorithms for Generalized Eigenproblems Via the Inverse-Free Iteration , 2006, PARA.
[33] Ming Gu,et al. Efficient Algorithms for Computing a Strong Rank-Revealing QR Factorization , 1996, SIAM J. Sci. Comput..
[34] Bruno Lang,et al. A Parallel Algorithm for Reducing Symmetric Banded Matrices to Tridiagonal Form , 1993, SIAM J. Sci. Comput..
[35] Christian H. Bischof,et al. Algorithm 807: The SBR Toolbox—software for successive band reduction , 2000, TOMS.
[36] Xiaobai Sun,et al. The PRISM project: infrastructure and algorithms for parallel eigensolvers , 1993, Proceedings of Scalable Parallel Libraries Conference.
[37] L. Trefethen,et al. Spectra and Pseudospectra , 2020 .
[38] Jeremy D. Frens,et al. QR factorization with Morton-ordered quadtree matrices for memory re-use and parallelism , 2003, PPoPP '03.
[39] James Demmel,et al. Minimizing Communication in Linear Algebra , 2009, ArXiv.
[40] Ed Anderson,et al. LAPACK Users' Guide , 1995 .
[41] S. Godunov. Problem of the dichotomy of the spectrum of a matrix , 1986 .
[42] Inderjit S. Dhillon,et al. The design and implementation of the MRRR algorithm , 2006, TOMS.
[43] Robert A. van de Geijn,et al. SUMMA: scalable universal matrix multiplication algorithm , 1995, Concurr. Pract. Exp..
[44] Paul Willems,et al. On MR3-type Algorithms for the Tridiagonal Symmetric Eigenproblem and the Bidiagonal SVD , 2018 .
[45] J. D. Roberts,et al. Linear model reduction and solution of the algebraic Riccati equation by use of the sign function , 1980 .
[46] Lars Karlsson,et al. Parallel two-stage reduction to Hessenberg form using dynamic scheduling on shared-memory architectures , 2011, Parallel Comput..
[47] Jack J. Dongarra,et al. Scheduling two-sided transformations using tile algorithms on multicore architectures , 2010, Sci. Program..
[48] James Demmel,et al. ScaLAPACK: A Portable Linear Algebra Library for Distributed Memory Computers - Design Issues and Performance , 1995, Proceedings of the 1996 ACM/IEEE Conference on Supercomputing.
[49] Inderjit S. Dhillon,et al. Orthogonal Eigenvectors and Relative Gaps , 2003, SIAM J. Matrix Anal. Appl..
[50] Robert H. Halstead,et al. Matrix Computations , 2011, Encyclopedia of Parallel Computing.
[51] H. Schwarz. Tridiagonalization of a symetric band matrix , 1968 .
[52] Matteo Frigo,et al. Cache-oblivious algorithms , 1999, 40th Annual Symposium on Foundations of Computer Science (Cat. No.99CB37039).
[53] Brian D. Sutton,et al. The stochastic operator approach to random matrix theory , 2005 .