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SIAMMAX
2010
224views more  SIAMMAX 2010»
12 years 11 months ago
Robust Approximate Cholesky Factorization of Rank-Structured Symmetric Positive Definite Matrices
Abstract. Given a symmetric positive definite matrix A, we compute a structured approximate Cholesky factorization A RT R up to any desired accuracy, where R is an upper triangula...
Jianlin Xia, Ming Gu
CORR
2010
Springer
153views Education» more  CORR 2010»
13 years 4 months ago
Towards an Efficient Tile Matrix Inversion of Symmetric Positive Definite Matrices on Multicore Architectures
The algorithms in the current sequential numerical linear algebra libraries (e.g. LAPACK) do not parallelize well on multicore architectures. A new family of algorithms, the tile a...
Emmanuel Agullo, Henricus Bouwmeester, Jack Dongar...
ICPPW
2002
IEEE
13 years 9 months ago
Parallel Cholesky Factorization of a Block Tridiagonal Matrix
In this paper we discuss the parallel implementation of the Cholesky factorization of a positive definite symmetric matrix when that matrix is block tridiagonal. While parallel im...
Thuan D. Cao, John F. Hall, Robert A. van de Geijn
AMC
2006
80views more  AMC 2006»
13 years 4 months ago
Parallel preconditioned conjugate gradient optimization of the Rayleigh quotient for the solution of sparse eigenproblems
A parallel algorithm based on the multidimensional minimization of the Rayleigh quotient is proposed to evaluate the leftmost eigenpairs of the generalized symmetric positive defi...
Luca Bergamaschi, Angeles Martinez, Giorgio Pini
SIAMSC
2008
123views more  SIAMSC 2008»
13 years 4 months ago
Balanced Incomplete Factorization
In this paper we present a new incomplete factorization of a square matrix into triangular factors in which we get standard LU or LDLT factors (direct factors) and their inverses (...
Rafael Bru, José Marín, José ...