Efficient algorithms for computing the characteristic polynomial in a domain
Reads0
Chats0
TLDR
Two new sequential methods are given for computing the characteristic polynomial of an endomorphism of a free finite rank- n module over a domain, that require O( n 3 ) ring operations with exact divisions.About:
This article is published in Journal of Pure and Applied Algebra.The article was published on 2001-02-23 and is currently open access. It has received 11 citations till now. The article focuses on the topics: Characteristic polynomial & Matrix polynomial.read more
Citations
More filters
Proceedings ArticleDOI
Efficient computation of the characteristic polynomial
TL;DR: In this article, the authors presented two algorithms for finite fields: one is based on Krylov iterates and Gaussian elimination, and the second is an improvement of the second algorithm of Keller-Gehrig.
Posted Content
Efficient Computation of the Characteristic Polynomial
TL;DR: A probabilistic approach, based on integer minimal polynomial and Hensel factorization, is particularly well suited to sparse and/or structured matrices.
Book ChapterDOI
Effective Matrix Methods in Commutative Domains
TL;DR: Effective matrix methods for solving standard linear algebra problems in a commutative domains are discussed and two new methods for computing adjoined matrices are introduced.
Journal ArticleDOI
Characteristic and counting polynomials: modelling nonane isomers properties
TL;DR: In this article, the authors investigated the broad application of graph polynomials to the analysis of Henry's law constants (solubility) of nonane isomers, and showed that these constants can be modelled by using characteristic polynomial and counting poynomial on the distance matrix.
Journal ArticleDOI
Deterministic computation of the characteristic polynomial in the time of matrix multiplication
Vincent Neiger,Clément Pernet +1 more
TL;DR: This paper describes an algorithm which computes the characteristic polynomial of a matrix over a field within the same asymptotic complexity, up to constant factors, as the multiplication of two square matrices.
References
More filters
Book
A Course in Computational Algebraic Number Theory
TL;DR: The first seven chapters guide readers to the heart of current research in computational algebraic number theory, including recent algorithms for computing class groups and units, as well as elliptic curve computations, while the last three chapters survey factoring and primality testing methods.
Journal ArticleDOI
Computational Methods of Linear Algebra
Journal ArticleDOI
Fast Parallel Matrix Inversion Algorithms
TL;DR: The parallel arithmetic complexities of matrix inversion, solving systems of linear equations, computing determinants and computing the characteristic polynomial of a matrix are shown to have the same growth rate.
Journal ArticleDOI
Sylvester’s identity and multistep integer-preserving Gaussian elimination
TL;DR: In this paper, a method for integer-preserving elimination in systems of linear equations, AX = B, such that the magnitudes of the coefficients in the transformed matrices are minimized, and the computational efficiency is considerably increased in comparison with the corresponding ordinary (single-step) Gaussian elimination.
Journal ArticleDOI
Condensation of Determinants, Being a New and Brief Method for Computing their Arithmetical Values
TL;DR: In this paper, it is shown how to compute the arithmetical values of one or more determinants, such as 1, 3, -2 2, 1, 4 3, 5, -1.