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Algorithm 887: Cholmod, supernodal sparse cholesky factorization and update/downdate
 ACM Transactions on Mathematical Software
, 2008
"... CHOLMOD is a set of routines for factorizing sparse symmetric positive definite matrices of the form A or A A T, updating/downdating a sparse Cholesky factorization, solving linear systems, updating/downdating the solution to the triangular system Lx = b, and many other sparse matrix functions for b ..."
Abstract

Cited by 109 (8 self)
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CHOLMOD is a set of routines for factorizing sparse symmetric positive definite matrices of the form A or A A T, updating/downdating a sparse Cholesky factorization, solving linear systems, updating/downdating the solution to the triangular system Lx = b, and many other sparse matrix functions for both symmetric and unsymmetric matrices. Its supernodal Cholesky factorization relies on LAPACK and the Level3 BLAS, and obtains a substantial fraction of the peak performance of the BLAS. Both real and complex matrices are supported. CHOLMOD is written in ANSI/ISO C, with both C and MATLAB TM interfaces. It appears in MATLAB 7.2 as x=A\b when A is sparse symmetric positive definite, as well as in several other sparse matrix functions.
Algorithm 8xx: CHOLMOD, supernodal sparse Cholesky factorization and update/downdate
, 2006
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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/LDL T factors (direct factors) and their inverses (inverse factors) at the same time. Algorithmically, we derive this method from the approach based on the ShermanMorrison ..."
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Cited by 8 (0 self)
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In this paper we present a new incomplete factorization of a square matrix into triangular factors in which we get standard LU/LDL T factors (direct factors) and their inverses (inverse factors) at the same time. Algorithmically, we derive this method from the approach based on the ShermanMorrison formula [16]. In contrast to the RIF algorithm [9], the direct and inverse factors here directly influence each other throughout the computation. Consequently, the algorithm to compute the approximate factors may mutually balance dropping in the factors and control their conditioning in this way. Although we describe the theory behind the factorization for general nonsymmetric matrices, in implementation and experiments we restrict for clarity and conciseness only to the case when the system matrix is symmetric and positive definite. In this case, we call the new approximate LDL T factorization Balanced Incomplete Factorization (BIF). Our experimental results confirm that this factorization is very robust and may be useful in solving difficult illconditioned problems by preconditioned iterative methods. Moreover, the internal coupling of computation of direct and inverse factors results in much shorter setup times (times to compute approximate decomposition) than RIF, a method of a similar and very high level of robustness.
User Guide for CHOLMOD: a sparse Cholesky factorization and modification package
, 2009
"... CHOLMOD 1 is a set of routines for factorizing sparse symmetric positive definite matrices of the form A or AA T, updating/downdating a sparse Cholesky factorization, solving linear systems, updating/downdating the solution to the triangular system Lx = b, and many other sparse matrix functions for ..."
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Cited by 7 (0 self)
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CHOLMOD 1 is a set of routines for factorizing sparse symmetric positive definite matrices of the form A or AA T, updating/downdating a sparse Cholesky factorization, solving linear systems, updating/downdating the solution to the triangular system Lx = b, and many other sparse matrix functions for both symmetric and unsymmetric matrices. Its supernodal Cholesky factorization relies on LAPACK and the Level3 BLAS, and obtains a substantial fraction of the peak performance of the BLAS. Both real and complex matrices are supported. It also includes a nonsupernodal LDL T factorization method that can factorize symmetric indefinite matrices if all of their leading submatrices are wellconditioned (D is diagonal). CHOLMOD is written in ANSI/ISO C, with both C and MATLAB interfaces. This code works on Microsoft Windows and many versions of Unix and Linux. CHOLMOD Copyright c○20052009 by Timothy A. Davis. Portions are also copyrighted by William W. Hager (the Modify Module), and the University of Florida (the Partition and Core Modules). All Rights Reserved. Some of CHOLMOD’s Modules are distributed under the GNU General Public License, and others under the GNU Lesser General Public License. Refer to each Module for details. CHOLMOD is also available under other licenses that permit its use in proprietary applications; contact the authors for details. See
Animation manifolds for representing topological alteration
, 2008
"... An animation manifold encapsulates an animation sequence of surfaces contained within a higher dimensional manifold with one dimension being time. An iso–surface extracted from this structure is a frame of the animation sequence. In this dissertation I make an argument for the use of animation manif ..."
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An animation manifold encapsulates an animation sequence of surfaces contained within a higher dimensional manifold with one dimension being time. An iso–surface extracted from this structure is a frame of the animation sequence. In this dissertation I make an argument for the use of animation manifolds as a representation of complex animation sequences. In particular animation manifolds can represent transitions between shapes with differing topological structure and polygonal density. I introduce the animation manifold, and show how it can be constructed from a keyframe animation sequence and rendered using raytracing or graphics hardware. I then adapt three Laplacian editing frameworks to the higher dimensional context. I derive new boundary conditions for both primal and dual Laplacian methods, and present a technique to adaptively regularise the sampling of a deformed manifold after editing. The animation manifold can be used to represent a morph sequence between surfaces of arbitrary topology. I present a novel framework for achieving this by connecting planar cross sections in a higher dimension with a new constrained Delaunay triangulation. Topological alteration is achieved by using the Voronoi skeleton, a novel structure which provides a fast medial axis approximation.
A LargeScale Quadratic . . .
, 2008
"... Quadratic programming (QP) problems arise naturally in a variety of applications. In many cases, a good estimate of the solution may be available. It is desirable to be able to utilize such information in order to reduce the computational cost of finding the solution. Activeset methods for solving Q ..."
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Quadratic programming (QP) problems arise naturally in a variety of applications. In many cases, a good estimate of the solution may be available. It is desirable to be able to utilize such information in order to reduce the computational cost of finding the solution. Activeset methods for solving QP problems differ from interiorpoint methods in being able to take full advantage of such warmstart situations. QPBLU is a new Fortran 95 package for minimizing a convex quadratic function with linear constraints and bounds. QPBLU is an activeset method that uses blockLU updates of an initial KKT system to handle activeset changes as well as lowrank Hessian updates. It is intended for convex QP problems in which the linear constraint matrix is sparse and many degrees of freedom are expected at the solution. Warm start capabilities allow the solver to take advantage of good estimates of the optimal active set or solution. A key feature of the method is the ability to utilize a variety of sparse linear system packages to solve the KKT systems. QPBLU has been tested on QP problems derived from linear programming problems