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On Wiedemann's Method of Solving Sparse Linear Systems
TLDR
We show that the black box model for matrix sparsity is a significant abstraction. Expand
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LINBOX: A GENERIC LIBRARY FOR EXACT LINEAR ALGEBRA
TLDR
We describe the design of this generic library, sketch its current range of capabilities, and give several examples of its use. Expand
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Sparse Polynomial Interpolation in Nonstandard Bases
In this paper, we consider the problem of interpolating univariate polynomials over a field of characteristic zero that are sparse in (a) the Pochhammer basis or, (b) the Chebyshev basis. TheExpand
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Fast parallel computation of hermite and smith forms of polynomial matrices
Boolean circuits of polynomial size and polylogarithmic depth are given for computing the Hermite and Smith normal forms of polynomial matrices over finite fields and the field of rational numbers.Expand
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Certifying inconsistency of sparse linear systems
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Efficient matrix preconditioners for black box linear algebra
Abstract The main idea of the “black box” approach in exact linear algebra is to reduce matrix problems to the computation of minimum polynomials. In most cases preconditioning is necessary to obtainExpand
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Computing Simplicial Homology Based on Efficient Smith Normal Form Algorithms
TLDR
This paper focuses on methods for the computer calculation of the homology of finite simplicial complexes and its applications (see comments on the other invariants in Section 7). Expand
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An extension of Liouville's theorem on integration in finite terms
TLDR
We give an extension of Liouville's theorem by allowing, in addition to the elementary functions, special functions such as the error function, Fresnel integrals and the logarithmic integral to appear in the integral of an elementary function. Expand
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Computing the smith forms of integer matrices and solving related problems
The Smith form of an integer matrix plays an important role in the study of algebraic group theory, homology group theory, systems theory, matrix equivalence, Diophantine systems, and control theory.Expand
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Parallel algorithms for matrix normal forms
Abstract Here we offer a new randomized parallel algorithm that determines the Smith normal form of a matrix with entries being univariate polynomials with coefficients in an arbitrary field. TheExpand
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