Parallel Sparse Cholesky Fa torization

Task Scheduling using Block Dependency DAG of Block-Oriented Sparse Cholesky Factorizationy

The block-oriented sparse Cholesky factorization decomposes a sparse matrix into rectangular sub-blocks, and handles each block as a computational unit in order to increase data reuse in a hierarchical memory system. As well, the factorization method increases the degree of concurrency with the reduction of communication volumes so that it performs more eeciently on a distributed-memory multipr...

A Supernodal Cholesky Factorization Algorithm for Shared-Memory Multiprocessors

This paper presents a new left-looking parallel sparse Cholesky fac,torization algorithm for shared-memory MIMD multiprocessors. The algorithm is particularly well-suited for vector supercomputers with multiple processors, such as the Cray Y-MP. The new algorithm uses supernodes in the Cholesky factor to improve performance by reducing indirect addressing and memory traffic. Earlier factorizati...

Computing Row and Column Counts for Sparse QR and LU Fa torization

On Evaluating Parallel Sparse Cholesky Factorizations

Though many parallel implementations of sparse Cholesky factorization with the experimental results accompanied have been proposed, it seems hard to evaluate the performance of these factorization methods theoretically because of the irregular structure of sparse matrices. This paper is an attempt to such research. On the basis of the criteria of parallel computation and communication time, we ...

Scalable Parallel Algorithms for Solving Sparse Systems of Linear Equations∗

We have developed a highly parallel sparse Cholesky factorization algorithm that substantially improves the state of the art in parallel direct solution of sparse linear systems—both in terms of scalability and overall performance. It is a well known fact that dense matrix factorization scales well and can be implemented efficiently on parallel computers. However, it had been a challenge to dev...