A generalization of the fast LUP matrix decomposition algorithm and applications

Ibarra, Óscar H.; Moran, Shlomo; Hui, Roger K. W.

doi:10.1016/0196-6774(82)90007-4

Cited by 112 publications

(94 citation statements)

References 2 publications

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“…We let ω be a feasible exponent for linear algebra, in the sense that matrices of size n can be multiplied in O(n ω ) base ring operations over any ring; the best bound to date is ω < 2.38 [16,31]. We will have to compute rank and rank pro le of dense matrices; the cost reduces to that of matrix multiplication [25].…”

Section: Basic Resultsmentioning

confidence: 99%

Algorithms for Structured Linear Systems Solving and Their Implementation

Hyun

Lebreton

Schost

2017

Proceedings of the 2017 ACM International Symposium on Symbolic and Algebraic Computation

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ABSTRACTere exists a vast literature dedicated to algorithms for structured matrices, but relatively few descriptions of actual implementations and their practical performance. In this paper, we consider the problem of solving Cauchy-like systems, and its application to mosaic Toeplitz systems, in two contexts: rst in the unit cost model (which is a good model for computations over nite elds), then over Q. We introduce new variants of previous algorithms and describe an implementation of these techniques and its practical behavior. We pay a special a ention to particular cases such as the computation of algebraic approximants.

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Section: Basic Resultsmentioning

confidence: 99%

Algorithms for Structured Linear Systems Solving and Their Implementation

Hyun

Lebreton

Schost

2017

Proceedings of the 2017 ACM International Symposium on Symbolic and Algebraic Computation

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“…Therefore, we can find a basis for the null space of C by finding bases for the null spaces of C and C . This can be done in O(s ω−1 t) time [24], where ω denotes the exponent of matrix multiplication. Thus, the running time of algorithm Randomized-SubtreeIsomorphism is O( n …”

Section: Lemma 44 For Every Heavy Vertexmentioning

confidence: 99%

Faster Subtree Isomorphism

Shamir

Tsur

1999

Journal of Algorithms

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We study the subtree isomorphism problem: Given trees H and G, find a subtree of G which is isomorphic to H or decide that there is no such subtree. We give an O((k 1.5 / log k)n)-time algorithm for this problem, where k and n are the number of vertices in H and G, respectively. This improves over the O(k 1.5 n) algorithms of Chung and Matula. We also give a randomized (Las Vegas) O(k 1.376 n)-time algorithm for the decision problem.

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“…Step 2 of the algorithm may require inversion of order s matrices [4]. Hence, if we take F to be the field of rational numbers (with C = ( 1,2, .…”

Section: ~@(Ag@))mentioning

confidence: 99%

“…The best bound on /3 currently claimed is 2.49+, and recent developments may reduce this bound further [5]. Our algorithms use the following result in [4]:…”

Section: Introductionmentioning

confidence: 99%