On the storage requirement in the out-of-core multifrontal method for sparse factorization
ACM Transactions on Mathematical Software (TOMS)
Direct methods for sparse matrices
Direct methods for sparse matrices
An adaptive general sparse out-of-core cholesky factorization scheme
SIAM Journal on Scientific and Statistical Computing
The influence of relaxed supernode partitions on the multifrontal method
ACM Transactions on Mathematical Software (TOMS)
The role of elimination trees in sparse factorization
SIAM Journal on Matrix Analysis and Applications
ACM Transactions on Mathematical Software (TOMS)
On finding supernodes for sparse matrix computations
SIAM Journal on Matrix Analysis and Applications
Block sparse Cholesky algorithms on advanced uniprocessor computers
SIAM Journal on Scientific Computing
Proceedings of the fourth workshop on I/O in parallel and distributed systems: part of the federated computing research conference
An Approximate Minimum Degree Ordering Algorithm
SIAM Journal on Matrix Analysis and Applications
Locality of Reference in LU Decomposition with Partial Pivoting
SIAM Journal on Matrix Analysis and Applications
A Fast and High Quality Multilevel Scheme for Partitioning Irregular Graphs
SIAM Journal on Scientific Computing
Efficient Methods for Out-of-Core Sparse Cholesky Factorization
SIAM Journal on Scientific Computing
A New Implementation of Sparse Gaussian Elimination
ACM Transactions on Mathematical Software (TOMS)
The Multifrontal Solution of Indefinite Sparse Symmetric Linear
ACM Transactions on Mathematical Software (TOMS)
Computer Solution of Large Sparse Positive Definite
Computer Solution of Large Sparse Positive Definite
A Fully Asynchronous Multifrontal Solver Using Distributed Dynamic Scheduling
SIAM Journal on Matrix Analysis and Applications
Very large electronic structure calculations using an out-of-core filter-diagonalization method
Journal of Computational Physics
Automatically Tuned Linear Algebra Software
Automatically Tuned Linear Algebra Software
Algebraic analysis of high-pass quantization
ACM Transactions on Graphics (TOG)
An out-of-core sparse symmetric-indefinite factorization method
ACM Transactions on Mathematical Software (TOMS)
ACM Transactions on Mathematical Software (TOMS)
Experiences of sparse direct symmetric solvers
ACM Transactions on Mathematical Software (TOMS)
PyTrilinos: High-performance distributed-memory solvers for Python
ACM Transactions on Mathematical Software (TOMS)
On the design of interfaces to sparse direct solvers
ACM Transactions on Mathematical Software (TOMS)
Algorithm 887: CHOLMOD, Supernodal Sparse Cholesky Factorization and Update/Downdate
ACM Transactions on Mathematical Software (TOMS)
Dynamic Supernodes in Sparse Cholesky Update/Downdate and Triangular Solves
ACM Transactions on Mathematical Software (TOMS)
An out-of-core sparse Cholesky solver
ACM Transactions on Mathematical Software (TOMS)
On the I/O Volume in Out-of-Core Multifrontal Methods with a Flexible Allocation Scheme
High Performance Computing for Computational Science - VECPAR 2008
Scaling and pivoting in an out-of-core sparse direct solver
ACM Transactions on Mathematical Software (TOMS)
Analysis of the solution phase of a parallel multifrontal approach
Parallel Computing
The design of a new out-of-core multifrontal solver
PARA'06 Proceedings of the 8th international conference on Applied parallel computing: state of the art in scientific computing
Reducing the I/O volume in an out-of-core sparse multifrontal solver
HiPC'07 Proceedings of the 14th international conference on High performance computing
A supernodal out-of-core sparse Gaussian-elimination method
PPAM'07 Proceedings of the 7th international conference on Parallel processing and applied mathematics
Sparse non-linear least squares optimization for geometric vision
ECCV'10 Proceedings of the 11th European conference on Computer vision: Part II
Reducing the I/O Volume in Sparse Out-of-core Multifrontal Methods
SIAM Journal on Scientific Computing
A preliminary out-of-core extension of a parallel multifrontal solver
Euro-Par'06 Proceedings of the 12th international conference on Parallel Processing
Model order reduction for large scale engineering models developed in ANSYS
PARA'04 Proceedings of the 7th international conference on Applied Parallel Computing: state of the Art in Scientific Computing
PARA'04 Proceedings of the 7th international conference on Applied Parallel Computing: state of the Art in Scientific Computing
Managing data-movement for effective shared-memory parallelization of out-of-core sparse solvers
SC '12 Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis
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We describe a new out-of-core sparse Cholesky factorization method. The new method uses the elimination tree to partition the matrix, an advanced subtree-scheduling algorithm, and both right-looking and left-looking updates. The implementation of the new method is efficient and robust. On a 2 GHz personal computer with 768 MB of main memory, the code can easily factor matrices with factors of up to 48 GB, usually at rates above 1 Gflop/s. For example, the code can factor audikw, currenly the largest matrix in any matrix collection (factor size over 10 GB), in a little over an hour, and can factor a matrix whose graph is a 140-by-140-by-140 mesh in about 12 hours (factor size around 27 GB).