Approximate iterations for structured matrices
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Boris N. Khoromskij | Eugene E. Tyrtyshnikov | Wolfgang Hackbusch | W. Hackbusch | E. Tyrtyshnikov | B. Khoromskij
[1] Martin J. Mohlenkamp,et al. Numerical operator calculus in higher dimensions , 2002, Proceedings of the National Academy of Sciences of the United States of America.
[2] W. Hackbusch,et al. A Sparse ℋ-Matrix Arithmetic. , 2000, Computing.
[3] Charles R. Johnson,et al. Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.
[4] Martin J. Mohlenkamp,et al. Fast Spectral Projection Algorithms for Density-Matrix Computations , 1999 .
[5] N. Higham. Newton's method for the matrix square root , 1986 .
[6] Lars Grasedyck,et al. Existence and Computation of a Low Kronecker-Rank Approximant to the Solution of a Tensor System with Tensor Right-Hand Side , 2003 .
[7] Eugene E. Tyrtyshnikov,et al. Matrix‐free iterative solution strategies for large dense linear systems , 1997 .
[8] G. Beylkin,et al. Wave propagation using bases for bandlimited functions , 2005 .
[9] Boris N. Khoromskij,et al. Hierarchical Kronecker tensor-product approximations , 2005, J. Num. Math..
[10] Martin J. Mohlenkamp,et al. Algorithms for Numerical Analysis in High Dimensions , 2005, SIAM J. Sci. Comput..
[11] Boris N. Khoromskij,et al. Low-rank Kronecker-product Approximation to Multi-dimensional Nonlocal Operators. Part II. HKT Representation of Certain Operators , 2005, Computing.
[12] Wolfgang Hackbusch,et al. A Sparse Matrix Arithmetic Based on H-Matrices. Part I: Introduction to H-Matrices , 1999, Computing.
[13] Bradley K. Alpert,et al. Adaptive solution of partial di erential equations in multiwavelet bases , 2002 .
[14] Judith M. Ford,et al. Combining Kronecker Product Approximation with Discrete Wavelet Transforms to Solve Dense, Function-Related Linear Systems , 2003, SIAM J. Sci. Comput..
[15] Eugene E. Tyrtyshnikov. Mosaic Ranks and Skeletons , 1996, WNAA.
[16] Lars Grasedyck,et al. Existence and Computation of Low Kronecker-Rank Approximations for Large Linear Systems of Tensor Product Structure , 2004, Computing.
[17] W. Hackbusch,et al. Numerische Mathematik Existence of H-matrix approximants to the inverse FE-matrix of elliptic operators with L ∞-coefficients , 2002 .
[18] Boris N. Khoromskij,et al. Low-rank Kronecker-product Approximation to Multi-dimensional Nonlocal Operators. Part I. Separable Approximation of Multi-variate Functions , 2005, Computing.
[19] Boris N. Khoromskij,et al. A Sparse H-Matrix Arithmetic. Part II: Application to Multi-Dimensional Problems , 2000, Computing.
[20] Peter Lancaster,et al. Newton's Method for a Generalized Inverse Eigenvalue Problem , 1997, Numer. Linear Algebra Appl..
[21] S. Goreinov,et al. A Theory of Pseudoskeleton Approximations , 1997 .
[22] Boris N. Khoromskij,et al. Solution of Large Scale Algebraic Matrix Riccati Equations by Use of Hierarchical Matrices , 2003, Computing.
[23] Eugene E. Tyrtyshnikov,et al. Structured matrices: recent developments in theory and computation , 2001 .
[24] W. Hackbusch,et al. A sparse H -matrix arithmetic: general complexity estimates , 2000 .
[25] Judith M. Ford,et al. Matrix approximations and solvers using tensor products and non-standard wavelet transforms related to irregular grids , 2004 .
[26] W. Hackbusch. A Sparse Matrix Arithmetic Based on $\Cal H$-Matrices. Part I: Introduction to ${\Cal H}$-Matrices , 1999, Computing.
[27] G. Stewart,et al. Matrix Perturbation Theory , 1990 .
[28] Beatrice Meini,et al. Solving block banded block Toeplitz systems with structured blocks: algorithms and applications , 2001 .
[29] Ivan P. Gavrilyuk,et al. $\mathcal{H}$-Matrix approximation for the operator exponential with applications , 2002, Numerische Mathematik.
[30] R. Byers,et al. The Matrix Sign Function Method and the Computation of Invariant Subspaces , 1997, SIAM J. Matrix Anal. Appl..
[31] Eugene E. Tyrtyshnikov,et al. Incomplete Cross Approximation in the Mosaic-Skeleton Method , 2000, Computing.
[32] Ivan Oseledets,et al. Approximate inversion of matrices in the process of solving a hypersingular integral equation , 2005 .
[33] E. Tyrtyshnikov,et al. Tensor properties of multilevel Toeplitz and related matrices , 2006 .
[34] V. Pan. Structured Matrices and Polynomials , 2001 .
[35] Ivan P. Gavrilyuk,et al. Hierarchical Tensor-Product Approximation to the Inverse and Related Operators for High-Dimensional Elliptic Problems , 2004, Computing.
[36] James Hardy Wilkinson,et al. Rounding errors in algebraic processes , 1964, IFIP Congress.
[37] E. Tyrtyshnikov. Mosaic-Skeleton approximations , 1996 .
[38] Ivan P. Gavrilyuk,et al. Data-sparse approximation to a class of operator-valued functions , 2004, Math. Comput..
[39] HackbuschW.. A sparse matrix arithmetic based on H-matrices. Part I , 1999 .
[40] Ronald Kriemann,et al. Hierarchical Matrices Based on a Weak Admissibility Criterion , 2004, Computing.
[41] G. Schulz. Iterative Berechung der reziproken Matrix , 1933 .
[42] J HighamNicholas. Newton's method for the matrix square root , 1986 .
[43] A. Laub,et al. The matrix sign function , 1995, IEEE Trans. Autom. Control..
[44] Victor Y. Pan,et al. Newton's iteration for the inversion of structured matrices , 2001 .
[45] E. Tyrtyshnikov. Tensor approximations of matrices generated by asymptotically smooth functions , 2003 .
[46] Ivan P. Gavrilyuk,et al. Data-sparse approximation to the operator-valued functions of elliptic operator , 2003, Math. Comput..
[47] Wolfgang Hackbusch,et al. Construction and Arithmetics of H-Matrices , 2003, Computing.
[48] Ilghiz Ibraghimov,et al. Application of the three‐way decomposition for matrix compression , 2002, Numer. Linear Algebra Appl..
[49] Alex Yu. Yeremin,et al. Matrix-free iterative solution strategies for large dense linear systems , 1997, Numer. Linear Algebra Appl..
[50] E. Tyrtyshnikov. Kronecker-product approximations for some function-related matrices , 2004 .
[51] Joos Vandewalle,et al. A Multilinear Singular Value Decomposition , 2000, SIAM J. Matrix Anal. Appl..
[52] C. Loan,et al. Approximation with Kronecker Products , 1992 .
[53] Nicholas J. Higham,et al. Stable iterations for the matrix square root , 1997, Numerical Algorithms.