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Locality Of Reference In Lu Decomposition With Partial Pivoting
 SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS
, 1997
"... This paper presents a new partitioned algorithm for LU decomposition with partial pivoting. The new algorithm, called the recursively partitioned algorithm, is based on a recursive partitioning of the matrix. The paper analyzes the locality of reference in the new algorithm and the locality of refer ..."
Abstract

Cited by 96 (10 self)
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This paper presents a new partitioned algorithm for LU decomposition with partial pivoting. The new algorithm, called the recursively partitioned algorithm, is based on a recursive partitioning of the matrix. The paper analyzes the locality of reference in the new algorithm and the locality of reference in a known and widely used partitioned algorithm for LU decomposition called the rightlooking algorithm. The analysis reveals that the new algorithm performs a factor of $\Theta(\sqrt{M/n})$ fewer I/O operations (or cache misses) than the rightlooking algorithm, where $n$ is the order of the matrix and $M$ is the size of primary memory. The analysis also determines the optimal block size for the rightlooking algorithm. Experimental comparisons between the new algorithm and the rightlooking algorithm show that an implementation of the new algorithm outperforms a similarly coded rightlooking algorithm on six different RISC architectures, that the new algorithm performs fewer cache misses than any other algorithm tested, and that it benefits more from Strassen's matrixmultiplication algorithm.
A Survey of OutofCore Algorithms in Numerical Linear Algebra
 DIMACS SERIES IN DISCRETE MATHEMATICS AND THEORETICAL COMPUTER SCIENCE
, 1999
"... This paper surveys algorithms that efficiently solve linear equations or compute eigenvalues even when the matrices involved are too large to fit in the main memory of the computer and must be stored on disks. The paper focuses on scheduling techniques that result in mostly sequential data acces ..."
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Cited by 59 (3 self)
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This paper surveys algorithms that efficiently solve linear equations or compute eigenvalues even when the matrices involved are too large to fit in the main memory of the computer and must be stored on disks. The paper focuses on scheduling techniques that result in mostly sequential data accesses and in data reuse, and on techniques for transforming algorithms that cannot be effectively scheduled. The survey covers outofcore algorithms for solving dense systems of linear equations, for the direct and iterative solution of sparse systems, for computing eigenvalues, for fast Fourier transforms, and for Nbody computations. The paper also discusses reasonable assumptions on memory size, approaches for the analysis of outofcore algorithms, and relationships between outofcore, cacheaware, and parallel algorithms.
Quantitative Performance Modeling of Scientific Computations and Creating Locality in Numerical Algorithms
, 1995
"... you design an efficient outofcore iterative algorithm? These are the two questions answered in this thesis. ..."
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you design an efficient outofcore iterative algorithm? These are the two questions answered in this thesis.