# Efficient Methods for Out-of-Core Sparse Cholesky Factorization

@article{Rothberg1999EfficientMF, title={Efficient Methods for Out-of-Core Sparse Cholesky Factorization}, author={Edward E. Rothberg and Robert S. Schreiber}, journal={SIAM J. Sci. Comput.}, year={1999}, volume={21}, pages={129-144} }

We consider the problem of sparse Cholesky factorization with limited main memory. The goal is to efficiently factor matrices whose Cholesky factors essentially fill the available disk storage, using very little memory (as little as 16 Megabytes (MBytes)). This would enable very large industrial problems to be solved with workstations of very modest cost.
We consider three candidate algorithms. Each is based on a partitioning of the matrix into panels. The first is a robust, out-of-core…

## 42 Citations

### An out-of-core sparse Cholesky solver

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The design and development of the first release of a new symmetric direct solver that aims to circumvent this limitation by allowing the system matrix, intermediate data, and the matrix factors to be stored externally.

### The design and implementation of a new out-of-core sparse cholesky factorization method

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- 2004

A new out-of-core sparse Cholesky factorization method that uses the elimination tree to partition the matrix, an advanced subtree-scheduling algorithm, and both right-looking and left-looking updates is described.

### Towards a Parallel Out-of-core Multifrontal Solver: Preliminary Study

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- 2007

A prototype implementation of an out-of-core extension to a parallel multifrontal solver (MUMPS), where disk is used to store data that cannot fit in memory, and it is shown that, by storing the factors to disk, larger problems can be solved on limited-memory machines with reasonable performance.

### Scaling and pivoting in an out-of-core sparse direct solver

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A new out-of-core multifrontal solver HSL_MA78 from the HSL mathematical software library that is designed to solve the unsymmetric sparse linear systems that arise from finite element applications is considered and how equilibration can be built into the solver without requiring the system matrix to be held in main memory is considered.

### The Design of I/O-Efficient Sparse Direct Solvers

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- 2001

This work guides us in designing a software library that implements an external memory sparse solver, and proves upper and lower bounds on these quantities for several model problems with useful sparsity.

### Reducing the I/O Volume in Sparse Out-of-core Multifrontal Methods

- Computer ScienceSIAM J. Sci. Comput.
- 2010

This paper shows how to process the task dependency graph of multifrontal methods in a way that minimizes the input/output (I/O) requirements and shows that efficient memory management algorithms can be applied to all the variants proposed.

### Locality of reference in sparse Cholesky factorization methods.

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- 2005

This paper analyzes the cache efficiency of two high-performance sparse Cholesky factorization algorithms: the multifrontal algorithm and the left-looking algorithm, and shows that while both algorithms sometimes enjoy a high level of data reuse in the cache, they are incomparable: there are matrices on which one is cache efficient and the other is not, and vice versa.

### On the Out-Of-Core Factorization of Large Sparse Matrices. (Méthodes directes hors-mémoire (out-of-core) pour la résolution de systèmes linéaires creux de grande taille)

- Computer Science
- 2008

This thesis proposes and studies various out-of-core models that aim at limiting the overhead due to data transfers between memory and disks on uniprocessor machines and focuses on a particular factorization method, the multifrontal method, that it shows allows to solve large sparse linear systems efficiently.

### Analysis of the solution phase of a parallel multifrontal approach

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