A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2012; you can also visit the original URL.
The file type is `application/pdf`

.

## Filters

##
###
A combined unifrontal/multifrontal method for unsymmetric sparse matrices

1999
*
ACM Transactions on Mathematical Software
*

The (uni-)frontal method avoids this extra work by

doi:10.1145/305658.287640
fatcat:5efpfopl4nam3dvvvxdydsvnam
*factorizing*the*matrix*with a single frontal*matrix*. Rows and columns are added to the frontal*matrix*, and pivot rows and columns are removed. ... In the*multifrontal*method, work on a frontal*matrix*can be suspended, the frontal*matrix*can be stored for later reuse, and a new frontal*matrix*can be generated. ... -j ) + max(i -j ) } , 5 {ai j #o aji#O where it is assumed the diagonal is nonzero so all terms in the summation are*non*-*negative*. ...##
###
A survey of direct methods for sparse linear systems

2016
*
Acta Numerica
*

sparse

doi:10.1017/s0962492916000076
fatcat:u4dqyjkjqnelll5e3ywm7lqkca
*matrix*problems. ... They exploit the sparsity of a*matrix*to solve problems economically: much faster and using far less memory than if all the entries of a*matrix*were stored and took part in explicit computations. ... QR*factorization*is an effective alternative.*Non*-*multifrontal*sparse QR methods are discussed in Section 7; here we present the*multifrontal*QR method. ...##
###
IMF: An Incomplete Multifrontal $LU$-Factorization for Element-Structured Sparse Linear Systems

2013
*
SIAM Journal on Scientific Computing
*

We propose an incomplete

doi:10.1137/100818996
fatcat:xutjmao4fnanropwxkfttjbogu
*multifrontal*LU -*factorization*(IMF) that extends supernodal*multifrontal*methods to incomplete*factorizations*. ... We propose an incomplete*multifrontal*LU -*factorization*(IMF) that extends supernodal*multifrontal*methods to incomplete*factorizations*. ... Furthermore, the ratio of the*non*-zeros in the block diagonal*matrix*to the total*non*-zeros in the preconditioner increases. ...##
###
A numerical evaluation of sparse direct solvers for the solution of large sparse symmetric linear systems of equations

2007
*
ACM Transactions on Mathematical Software
*

A

doi:10.1145/1236463.1236465
fatcat:zcqti6k6u5anbfht3sfwb2jibu
*factorization*phase that uses the pivot sequence to*factorize*the*matrix*(some codes scale the*matrix*prior to the*factorization*). 4. ... The*factorization*phase implements a modified*multifrontal*algorithm. ...##
###
AN EFFICIENT APPROACH FOR MULTIFRONTAL ALGORITHM TO SOLVE NON-POSITIVE-DEFINITE FINITE ELEMENT EQUATIONS IN ELECTROMAGNETIC PROBLEMS

2009
*
Electromagnetic Waves
*

Based on the method,

doi:10.2528/pier09070207
fatcat:lwu3nfokpjcsjespmbpp2iuawi
*multifrontal*(MF) algorithm is applied in*non*-positive-definite FEM computation. Numerical results show that the hybrid ECM/MF algorithm is stable and effective. ... The method can be used to decompose sparse symmetric*non*-positive-definite finite element (FEM) matrices. ... One of the significant advancements in direct methods for a sparse*matrix*solution is the development of the*multifrontal*(MF) algorithm [15] [16] [17] [18] . ...##
###
Multifrontal QR Factorization for Multicore Architectures over Runtime Systems
[chapter]

2013
*
Lecture Notes in Computer Science
*

This paper evaluates the usability of runtime systems for complex applications, namely, sparse

doi:10.1007/978-3-642-40047-6_53
fatcat:nuekjepqxbae7ocsklphedcyre
*matrix**multifrontal**factorizations*which constitute extremely irregular workloads, with tasks of different ... The*multifrontal*method, introduced by Duff and Reid [12] as a method for the*factorization*of sparse, symmetric linear systems, can be adapted to the QR*factorization*of a sparse*matrix*thanks to the ... fact that the R*factor*of a*matrix*A and the Cholesky*factor*of the normal equation*matrix*A T A share the same structure. ...##
###
Logarithmic barriers for sparse matrix cones

2013
*
Optimization Methods and Software
*

The algorithms are based on the

doi:10.1080/10556788.2012.684353
fatcat:k2apjixbnbeedj4d4ts7hkgfoi
*multifrontal*method for sparse Cholesky*factorization*. ... Linearized Cholesky*factorization*and*matrix*completion Let L(t), D(t) be the matrices in the*factorization*X(t) = X + tY = L(t)D(t)L(t) T and let U i (t) be the ith update*matrix*in the*multifrontal**factorization*... In the context of*multifrontal**factorizations*, the grouping into supernodes has the advantage that only one frontal*matrix*is required per supernode. ...##
###
Sweeping Preconditioner for the Helmholtz Equation: Moving Perfectly Matched Layers
[article]

2010
*
arXiv
*
pre-print

Applying each Schur complement

arXiv:1007.4291v2
fatcat:fvknv3b6inayfbkf3hkiokjkxa
*matrix*is equivalent to solving a quasi-1D problem with a banded LU*factorization*in the 2D case and to solving a quasi-2D problem with a*multifrontal*method in the 3D case ... The central idea of this paper is to approximate the Schur complement matrices of the*factorization*using moving perfectly matched layers (PMLs) introduced in the interior of the domain. ... In practice, instead of generating the sweeping*factorization*of the original*matrix*A, we choose to generate the*factorization*for the*matrix*A α associated with the modified Helmholtz equation ∆u(x) ...##
###
A fast direct solver for elliptic problems on general meshes in 2D

2012
*
Journal of Computational Physics
*

We follow the approach in Xia et al. (2009) on combining the

doi:10.1016/j.jcp.2011.10.013
fatcat:dy766mrwrrfbbft2qigpddp7hi
*multifrontal*method with hierarchical matrices. ... However, the efficiency of the sparse Cholesky decomposition depends on choosing a reordering to reduce fill-in of*non*-zeros in the*factors*. ... Moreover, most of*matrix*operations such as*matrix*-vector product,*matrix*addition,*matrix*multiplication,*matrix*inversion, and some*matrix**factorizations*, can be carried out in the hierarchical*matrix*...##
###
A parallel formulation of interior point algorithms

1994
*
Supercomputing, Proceedings
*

In our parallel interior point algorithm, we use our recently developed parallel

doi:10.1145/602805.602808
fatcat:23vhjjrnfrfe7lx4khfmtnu5ja
*multifrontal*algorithm that has the smallest communication overhead over all parallel algorithms for Cholesky*factorization*... A key component of the interior point algorithm is the solution of a sparse system of linear equations using Cholesky*factorization*. ...*Multifrontal*Method Let M be an m m symmetric positive de nite*matrix*and L be its Cholesky*factor*. ...##
###
A parallel formulation of interior point algorithms

1994
*
Supercomputing, Proceedings
*

In our parallel interior point algorithm, we use our recently developed parallel

doi:10.1145/602770.602808
fatcat:joxeq6lb7fh45jefcwyhdskrua
*multifrontal*algorithm that has the smallest communication overhead over all parallel algorithms for Cholesky*factorization*... A key component of the interior point algorithm is the solution of a sparse system of linear equations using Cholesky*factorization*. ...*Multifrontal*Method Let M be an m m symmetric positive de nite*matrix*and L be its Cholesky*factor*. ...##
###
Fast and Accurate Simulation of Multithreaded Sparse Linear Algebra Solvers

2015
*
2015 IEEE 21st International Conference on Parallel and Distributed Systems (ICPADS)
*

the QR

doi:10.1109/icpads.2015.67
dblp:conf/icpads/StanisicABGLLV15
fatcat:mscn54jpxzgfpmtyjcmelqn5j4
*factorization*of a sparse*matrix*thanks to the fact that the R*factor*of a*matrix*A and the Cholesky*factor*of the normal equation*matrix*A T A share the same structure under the hypothesis that ... In particular,*non*trivial results can be obtained such as the fact that the TF17*matrix*benefits much more from using several nodes than the sls*matrix*. B. ...##
###
Parallel computation of pseudospectra of large sparse matrices

2002
*
Parallel Computing
*

Computing the smallest singular value Given a large sparse

doi:10.1016/s0167-8191(01)00136-3
fatcat:3y3q7z4sfzbwhdwxyseqm5wmna
*matrix*A 2 C nÂn , we consider the*matrix*B 2 C 2nÂ2n B ¼ 0 A À1 A ÀH 0 : The eigenvalues of B are the singular values of A À1 and their*negatives*... As a trade-off, it converges only linearly with the convergence*factor*1=2. ...##
###
A sweeping preconditioner for Yee's finite difference approximation of time-harmonic Maxwell's equations

2012
*
Frontiers of Mathematics in China
*

. , n do
Let G m be as defined in (3.10) and H m be the

doi:10.1007/s11464-012-0191-8
fatcat:y6o563b2tfc5tezszn7tzcu3h4
*matrix*resulting from the finite difference discretization of (3.9). Construct the*multifrontal**factorization*of H m . ... using the*multifrontal**factorization*of H F . 5. for m = b + 1, . . . , n do u m = T m u m . ...##
###
Design of a Multicore Sparse Cholesky Factorization Using DAGs

2010
*
SIAM Journal on Scientific Computing
*

PaStiX [26, 27] is

doi:10.1137/090757216
fatcat:meflt2mkxfapzghp6fyg6ptmqa
*non*-*multifrontal*C/Pthreads/MPI code that is primarily designed for positive-definite systems. ... SuiteSparseQR [13] is a recent C++ sparse QR*factorization*package based on the*multifrontal*algorithm. ... When a*factorize*block or solve block task completes, we decrement the block's count to flag this event with a*negative*value. ...
« Previous

*Showing results 1 — 15 out of 305 results*