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Cholesky factorization
 Interdisciplinary Reviews: Computational Statistics
, 2009
"... This article, aimed at a general audience of computational scientists, surveys the Cholesky factorization for symmetric positive definite matrices, covering algorithms for computing it, the numerical stability of the algorithms, and updating and downdating of the factorization. Cholesky factoriza ..."
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This article, aimed at a general audience of computational scientists, surveys the Cholesky factorization for symmetric positive definite matrices, covering algorithms for computing it, the numerical stability of the algorithms, and updating and downdating of the factorization. Cholesky
Cholesky factor GARCH
 Mimeo. Quantitative Micro Software
"... In this paper, I propose a new class of multivariate GARCH models that specify the dynamics in terms of the cholesky factor of the conditional covariance. In the special case of a univariate model, this is equivalent to specifying the dynamics of the conditional standard deviation. The main advantag ..."
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In this paper, I propose a new class of multivariate GARCH models that specify the dynamics in terms of the cholesky factor of the conditional covariance. In the special case of a univariate model, this is equivalent to specifying the dynamics of the conditional standard deviation. The main
On the Perturbation of LU and Cholesky Factors
 of LU, Cholesky, and QR Factorizations, &quot; in preparation
, 1997
"... In a recent paper, Chang and Paige have shown that the usual perturbation bounds for Cholesky factors can systematically overestimate the errors. In this note we sharpen their results and extend them to the factors of the LU decomposition. The results are based on a new formula for the first order t ..."
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In a recent paper, Chang and Paige have shown that the usual perturbation bounds for Cholesky factors can systematically overestimate the errors. In this note we sharpen their results and extend them to the factors of the LU decomposition. The results are based on a new formula for the first order
An Improved Incomplete Cholesky Factorization
 ACM Trans. Math. Software
, 1995
"... Incomplete factorization has been shown to be a good preconditioner for the conjugate gradient method on a wide variety of problems. It is well known that allowing some fillin during the incomplete factorization can significantly reduce the number of iterations needed for convergence. Allowing fill ..."
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Cited by 29 (0 self)
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such strategies impractical to use in many situations. In this paper we motivate, and then present, two "blackbox" strategies that significantly increase the effectiveness of incomplete Cholesky factorization as a preconditioner. These strategies require no parameters from the user and do not increase
Level3 Cholesky Factorization and . . .
, 2011
"... ... block factorization algorithm. We discuss four Level3 routines called DPOTF3i, i = a,b,c,d,a new type of BLAS, for the factorization part of a block Cholesky factorization algorithm for use by LAPACK routine DPOTRF or for BPF (Blocked Packed Format) Cholesky factorization. The four routines DPO ..."
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... block factorization algorithm. We discuss four Level3 routines called DPOTF3i, i = a,b,c,d,a new type of BLAS, for the factorization part of a block Cholesky factorization algorithm for use by LAPACK routine DPOTRF or for BPF (Blocked Packed Format) Cholesky factorization. The four routines
Parallel Sparse Cholesky Factorization
"... In this paper we describe algorithms for the ordering and numerical factorization step in parallel sparse Cholesky factorization. Direct methods for solving sparse positive definite systems play an important role in many scientific applications such as linear programming and structual engineering. T ..."
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In this paper we describe algorithms for the ordering and numerical factorization step in parallel sparse Cholesky factorization. Direct methods for solving sparse positive definite systems play an important role in many scientific applications such as linear programming and structual engineering
GPU Accelerated Parallel Cholesky Factorization
"... Abstract. One of the fundamental problems in scientific computing is to find solutions for linear equation systems. For finite element problem, Cholesky factorization is often used to solve symmetric positive definite matrices. In this paper, Cholesky factorization is massively parallelized and thre ..."
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Abstract. One of the fundamental problems in scientific computing is to find solutions for linear equation systems. For finite element problem, Cholesky factorization is often used to solve symmetric positive definite matrices. In this paper, Cholesky factorization is massively parallelized
Modifying a Sparse Cholesky Factorization
, 1997
"... Given a sparse symmetric positive definite matrix AA T and an associated sparse Cholesky factorization LL T , we develop sparse techniques for obtaining the new factorization associated with either adding a column to A or deleting a column from A. Our techniques are based on an analysis and mani ..."
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Cited by 51 (15 self)
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Given a sparse symmetric positive definite matrix AA T and an associated sparse Cholesky factorization LL T , we develop sparse techniques for obtaining the new factorization associated with either adding a column to A or deleting a column from A. Our techniques are based on an analysis
Highly Parallel Sparse Cholesky Factorization
 SIAM Journal on Scientific and Statistical Computing
, 1992
"... We develop and compare several finegrained parallel algorithms to compute the Cholesky factorization of a sparse matrix. Our experimental implementations are on the Connection Machine, a distributedmemory SIMD machine whose programming model conceptually supplies one processor per data element. In ..."
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Cited by 49 (1 self)
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We develop and compare several finegrained parallel algorithms to compute the Cholesky factorization of a sparse matrix. Our experimental implementations are on the Connection Machine, a distributedmemory SIMD machine whose programming model conceptually supplies one processor per data element
Incomplete Cholesky Factorizations With Limited Memory
 SIAM J. SCI. COMPUT
, 1999
"... We propose an incomplete Cholesky factorization for the solution of largescale trust region subproblems and positive definite systems of linear equations. This factorization depends on a parameter p that specifies the amount of additional memory (in multiples of n, the dimension of the problem) tha ..."
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Cited by 42 (6 self)
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We propose an incomplete Cholesky factorization for the solution of largescale trust region subproblems and positive definite systems of linear equations. This factorization depends on a parameter p that specifies the amount of additional memory (in multiples of n, the dimension of the problem
Results 1  10
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