Fast and Efficient Parallel  Solution of Sparse Linear Systems

Fast and Efficient Parallel Solution of Sparse Linear Systems (1993)

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by Victor Pan , John Reif

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@MISC{Pan93fastand,
    author = {Victor Pan and John Reif},
    title = {Fast and Efficient Parallel Solution of Sparse Linear Systems},
    year = {1993}
}

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Citations

693	Matrix multiplication via arithmetic progressions - Coppersmith, Winograd - 1990
640	The Symmetric Eigenvalue Problem - Parlett - 1998
338	A separator theorem for planar graphs - Lipton, Tarjan - 1979
303	Gaussian elimination is not optimal - STRASSEN - 1969
154	Nested dissection of a regular finite element mesh - George - 1973
150	Generalized nested dissection - LIPTON, ROSE, et al. - 1979
140	Matching is as easy as matrix inversion - Mulmuley, Vazirani, et al. - 1987
104	personal communication - Miller
93	The computational complexity of algebraic and numeric problems - Borodin, Munro - 1975
88	A Graph-Theoretic Study of the Numerical Solution of Sparse Positive Definite Systems of Linear Equations - Rose - 1972
87	Fast algorithms for solving path problems - Tarjan - 1981
85	Efficient Parallel Solution of Linear Systems - Pan, Reif - 1985
74	Fast Parallel Matrix Inversion Algorithms - Csanky - 1976
62	A Unified Approach to Paths Problems - Tarjan - 1981
52	Sparse Cholesky factorization on a local memory multiprocessor - George, Heath, et al. - 1988
46	Solution of Partial Differential Equations on Vector and Parallel - Ortega, Vogt - 1985
44	Computer Solution of Large Sparse Positive De nite Systems - George, Liu - 1981
42	A survey of parallel algorithms for shared memory machines - Karp, Ramachandran - 1990
39	A new implementation of sparse gaussian elimination - SCHREIBER - 1982
38	On the asymptotic complexity of matrix multiplication - COPPERSMITH, WINOGRAD - 1982
36	The Symmetric Eigenvalue Problem (Prentice-Hall - Parlett - 1980
29	Parallel algorithmic techniques for combinatorial computation - Eppstein, Galil - 1988
28	The analysis of a nested dissection algorithm - Gilbert, Tarjan - 1987
27	A parallel algorithm for finding a separator in planar graphs - Gazit, Miller - 1987
24	How to multiply matrices faster - Pan - 1984
20	A Compact Row Storage Scheme for Cholesky Factors Using Elimination Trees - Liu - 1986
20	Parametrization of Newton's Iteration for Computations with Structured Matrices and Applications - PAN - 1990
19	How can we Speed up Matrix Multiplication - Pan - 1984
19	Partial and total matrix multiplication - SCHÖNHAGE - 1981
16	An improved Newton iteration for the generalized inverse of a matrix, with applications - PAN, SCHREIBER - 1991
15	On the problem of partitioning planar graphs - Djidjev - 1982
14	Nested dissection of a regular nite element mesh - George - 1973
13	Fast and efficient solution of path algebra problems - Pan, Reif - 1989
13	An improved parallel processor bound in fast matrix inversion - Preparata, Sarwate - 1978
12	Relative bilinear complexity and matrix multiplication. Journal fűr die reine und angewandte Mathematik (Crelles Journal - STRASSEN - 1987
11	Parallel evaluation of the determinant and of the inverse of a matrix - Galil, Pan - 1989
11	Solution of partial di erential equations on vector and parallel computers - Ortega, Voigt - 1985
10	Efficient Parallel Algorithms for the Exact Inversion of Integer Matrices - Pan, Fast - 1985
9	Fast parallel matrix - BORODIN, GATHEN, et al. - 1982
9	Parallel solution of sparse simultaneous linear equations - Calahan - 1973
9	New fast algorithms for matrix operations - PAN - 1980
9	The parallel computation of minimum cost paths in graphs by stream contraction - PAN, REIF - 1991
8	Improved processor bounds for combinatorial problems - GALIL, PAN - 1988
7	A note on iterative methods for generalized inversion of matrices - BEN-ISRAEL - 1966
7	Processor-e cient parallel solution of linear systems II: the positive characteristic and singular cases - Kaltofen, Pan - 1992
6	Complexity of parallel matrix computations”, Theoret - Pan - 1987
6	and Efficient Parallel Solution of Dense Linear Systems - Pan, Reif - 1989
5	Space and time efficient implementations of parallel nested dissection - Armon, Reif - 1992
5	Parallel Algorithms for Shared Memory - Karp, Ramachandran - 1990
5	The Solution of Mesh Equations on a Parallel Computer - LIU - 1978