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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 ..."
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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
Parallel and fully recursive multifrontal supernodal sparse cholesky
 Future Generation Computer Systems
, 2004
"... We describe the design, implementation, and performance of a new parallel sparse Cholesky factorization code. The code uses a multifrontal factorization strategy. Operations on small dense submatrices are performed using new densematrix subroutines that are part of the code, although the code can a ..."
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Cited by 19 (3 self)
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We describe the design, implementation, and performance of a new parallel sparse Cholesky factorization code. The code uses a multifrontal factorization strategy. Operations on small dense submatrices are performed using new densematrix subroutines that are part of the code, although the code can
LSQR: An Algorithm for Sparse Linear Equations and Sparse Least Squares
 ACM Trans. Math. Software
, 1982
"... An iterative method is given for solving Ax ~ffi b and minU Ax b 112, where the matrix A is large and sparse. The method is based on the bidiagonalization procedure of Golub and Kahan. It is analytically equivalent to the standard method of conjugate gradients, but possesses more favorable numerica ..."
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Cited by 649 (21 self)
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An iterative method is given for solving Ax ~ffi b and minU Ax b 112, where the matrix A is large and sparse. The method is based on the bidiagonalization procedure of Golub and Kahan. It is analytically equivalent to the standard method of conjugate gradients, but possesses more favorable
Dynamic supernodes in sparse Cholesky update/downdate and triangular solves
 ACM Trans. Math. Software
, 2006
"... The supernodal method for sparse Cholesky factorization represents the factor L as a set of supernodes, each consisting of a contiguous set of columns of L with identical nonzero pattern. A conventional supernode is stored as a dense submatrix. While this is suitable for sparse Cholesky factorizatio ..."
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Cited by 30 (10 self)
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The supernodal method for sparse Cholesky factorization represents the factor L as a set of supernodes, each consisting of a contiguous set of columns of L with identical nonzero pattern. A conventional supernode is stored as a dense submatrix. While this is suitable for sparse Cholesky
Sparse Bayesian Learning and the Relevance Vector Machine
, 2001
"... This paper introduces a general Bayesian framework for obtaining sparse solutions to regression and classication tasks utilising models linear in the parameters. Although this framework is fully general, we illustrate our approach with a particular specialisation that we denote the `relevance vec ..."
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Cited by 958 (5 self)
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This paper introduces a general Bayesian framework for obtaining sparse solutions to regression and classication tasks utilising models linear in the parameters. Although this framework is fully general, we illustrate our approach with a particular specialisation that we denote the `relevance
Direct and Incomplete Cholesky Factorizations with Static Supernodes
"... Incomplete factorizations of sparse symmetric positive definite (SSPD) matrices have been used to generate preconditioners for various iterative solvers. These solvers generally use preconditioners derived from the matrix system, , in order to reduce the total number of iterations until convergence. ..."
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Incomplete factorizations of sparse symmetric positive definite (SSPD) matrices have been used to generate preconditioners for various iterative solvers. These solvers generally use preconditioners derived from the matrix system, , in order to reduce the total number of iterations until convergence
A supernodal approach to sparse partial pivoting
 SIAM Journal on Matrix Analysis and Applications
, 1999
"... We investigate several ways to improve the performance of sparse LU factorization with partial pivoting, as used to solve unsymmetric linear systems. To perform most of the numerical computation in dense matrix kernels, we introduce the notion of unsymmetric supernodes. To better exploit the memory ..."
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Cited by 263 (25 self)
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We investigate several ways to improve the performance of sparse LU factorization with partial pivoting, as used to solve unsymmetric linear systems. To perform most of the numerical computation in dense matrix kernels, we introduce the notion of unsymmetric supernodes. To better exploit the memory
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
SNOPT: An SQP Algorithm For LargeScale Constrained Optimization
, 2002
"... Sequential quadratic programming (SQP) methods have proved highly effective for solving constrained optimization problems with smooth nonlinear functions in the objective and constraints. Here we consider problems with general inequality constraints (linear and nonlinear). We assume that first deriv ..."
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Cited by 582 (23 self)
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derivatives are available, and that the constraint gradients are sparse. We discuss
Bundle Adjustment  A Modern Synthesis
 VISION ALGORITHMS: THEORY AND PRACTICE, LNCS
, 2000
"... This paper is a survey of the theory and methods of photogrammetric bundle adjustment, aimed at potential implementors in the computer vision community. Bundle adjustment is the problem of refining a visual reconstruction to produce jointly optimal structure and viewing parameter estimates. Topics c ..."
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Cited by 555 (12 self)
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covered include: the choice of cost function and robustness; numerical optimization including sparse Newton methods, linearly convergent approximations, updating and recursive methods; gauge (datum) invariance; and quality control. The theory is developed for general robust cost functions rather than
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