## Distributed Matrix-Free Solution of Large Sparse Linear Systems over Finite Fields (1996)

Venue: | Algorithmica |

Citations: | 26 - 6 self |

### BibTeX

@ARTICLE{Kaltofen96distributedmatrix-free,

author = {E. Kaltofen and A. Lobo},

title = {Distributed Matrix-Free Solution of Large Sparse Linear Systems over Finite Fields},

journal = {Algorithmica},

year = {1996},

volume = {24},

pages = {331--348}

}

### Years of Citing Articles

### OpenURL

### Abstract

We describe a coarse-grain parallel software system for the homogeneous solution of linear systems. Our solutions are symbolic, i.e., exact rather than numerical approximations. Our implementation can be run on a network cluster of SPARC-20 computers and on an SP-2 multiprocessor. Detailed timings are presented for experiments with systems that arise in RSA challenge integer factoring efforts. For example, we can solve a 252; 222 \Theta 252; 222 system with about 11.04 million non-zero entries over the Galois field with 2 elements using 4 processors of an SP-2 multiprocessor, in about 26.5 hours CPU time. 1 Introduction The problem of solving large, unstructured, sparse linear systems using exact arithmetic arises in symbolic linear algebra and computational number theory. For example the sieve-based factoring of large integers can lead to systems containing over 569,000 equations and variables and over 26.5 million nonzero entries, that need to be solved over the Galois field of two...

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450 |
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Citation Context ...linear recurrence associated with f B;v . The minimum polynomial of fu tr B i vg i0 denoted by f B;v u , divides f B;v u . Each term of u tr B i v is an element of K and the BerlekampMassey algorithm =-=[2, 14]-=- can be employed to find f B;v u from the first 2N terms of fu tr B i vg i0 in time O(N 2 ) field operations. Wiedemann's algorithm is shown in figure (2.1). The components of vectors u and v are chos... |

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cient solution of linear systems of equations with recursive structure
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