Direct solution of large systems of linear equations

Wilson, Edward L.; Bathe, Klaus‐Jürgen; Doherty, William P.

doi:10.1016/0045-7949(74)90063-7

Cited by 66 publications

(14 citation statements)

References 5 publications

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“…These algorithms are essentially identical to dense partitioned algorithms, except that they do not operate on zero blocks. Cantin [8], Mondkar and Powell [41] and Wilson, Bathe and Doherty [60] all describe such algorithms in the early 1970s. The same idea can be used when the nonzeros are clustered in large dense blocks even when the blocks themselves are not clustered near the main diagonal.…”

Section: Sparse Matrix Factorizationsmentioning

confidence: 99%

A survey of out-of-core algorithms in numerical linear algebra

Toledo¹

1999

External Memory Algorithms

100

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Abstract. 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 out-of-core 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 N-body computations. The paper also discusses reasonable assumptions on memory size, approaches for the analysis of out-of-core algorithms, and relationships between out-of-core, cache-aware, and parallel algorithms.

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Section: Sparse Matrix Factorizationsmentioning

confidence: 99%

A survey of out-of-core algorithms in numerical linear algebra

Toledo¹

1999

External Memory Algorithms

100

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“…In a first stage, the matrix can be assembled, partitioned into blocks, with only one block present at a time in central core memory, the rest lying on secondary storage (tape or disk); in a second stage the blocks are read for factorization: Cantin (1971), Wilson et al (1974), Cheung and Khatua (1976), Mondkar andPowell (1974), Van Ingelandt (1979), Hasbany and Engelman (1979).…”

Section: Out Of Core Factorizationsmentioning

confidence: 99%

Implementation of Finite Element Methods for Navier-Stokes Equations

Thomasset¹

1981

230

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“…Since the ÿrst and the last three rows of the sti ness matrices in Figures 4 and 5 coincide, in this case the reactions can also be obtained by (9). Case 3.…”

mentioning

confidence: 94%

“…Thus, ÿrst the unknown displacements are obtained from (8), and next the reactions can be obtained by (9). Case 2.…”

mentioning

confidence: 99%

Updating inverses in matrix analysis of structures

Castillo

Cobo

Fernández‐Canteli

et al. 1998

Int. J. Numer. Meth. Engng.

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We deal with the problem of updating inverses. Several methods which allow calculating the inverse of a matrix when one or several rows (columns) are changed, or one or several rows and the same number of columns are added or removed are given. They are based on a method for calculating inverses given by Jubete and Castillo, which uses the concept of orthogonal sets, and lead to a considerable saving in computational power. The methods are ideal for being used in the design process of structures, where sti ness matrices are sequentially modiÿed by simply changing rows (columns), and adding or removing rows and columns, as the result of modifying the geometric or structural characteristics of its pieces, the structure's degrees of freedom, and/or the boundary conditions. Some examples of simple structures are given to illustrate the methodology. Finally, a discussion about its practical application and some conclusions and recommendations are given. ? 1998 John Wiley & Sons, Ltd.

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Direct solution of large systems of linear equations

Cited by 66 publications

References 5 publications

A survey of out-of-core algorithms in numerical linear algebra

A survey of out-of-core algorithms in numerical linear algebra

Implementation of Finite Element Methods for Navier-Stokes Equations

Updating inverses in matrix analysis of structures

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