Computing Spectral Elimination Ideals
نویسنده
چکیده
We present here an overview of the hypermatrix spectral decomposition deduced from the Bhattacharya-Mesner hypermatrix algebra [BM1, BM2]. We describe necessary and sufficient conditions for the existence of a spectral decomposition. We further extend to hypermatrices the notion of resolution of identity and use them to derive hypermatrix analog of matrix spectral bounds. Finally we describe an algorithm for computing generators of the spectral elimination ideals which considerably improves on Groebner basis computation suggested in [GER].
منابع مشابه
Chebyshev Spectral Collocation Method for Computing Numerical Solution of Telegraph Equation
In this paper, the Chebyshev spectral collocation method(CSCM) for one-dimensional linear hyperbolic telegraph equation is presented. Chebyshev spectral collocation method have become very useful in providing highly accurate solutions to partial differential equations. A straightforward implementation of these methods involves the use of spectral differentiation matrices. Firstly, we transform ...
متن کاملComputing SAGB-Gröbner Basis of Ideals of Invariant Rings by Using Gaussian Elimination
The link between Gröbner basis and linear algebra was described by Lazard [4,5] where he realized the Gröbner basis computation could be archived by applying Gaussian elimination over Macaulay’s matrix . In this paper, we indicate how same technique may be used to SAGBIGröbner basis computations in invariant rings. . Keywords— Gröbner basis, SAGBIGröbner basis, reduction, Invariant ring, permut...
متن کاملEuclid's Algorithm, Guass' Elimination and Buchberger's Algorithm
It is known that Euclid’s algorithm, Guass’ elimination and Buchberger’s algorithm play important roles in algorithmic number theory, symbolic computation and cryptography, and even in science and engineering. The aim of this paper is to reveal again the relations of these three algorithms, and, simplify Buchberger’s algorithm without using multivariate division algorithm. We obtain an algorith...
متن کاملGenerating Loop Invariants by Computing Vanishing Ideals of Sample Points
Loop invariants play a very important role in proving correctness of programs. In this paper, we address the problem of generating invariants of polynomial loop programs. We present a new approach, for generating polynomial equation invariants of polynomial loop programs through computing vanishing ideals of sample points. We apply rational function interpolation, based on early termination tec...
متن کاملFUZZY OBSTINATE IDEALS IN MV-ALGEBRAS
In this paper, we introduce the notion of fuzzy obstinate ideals in MV -algebras. Some properties of fuzzy obstinateideals are given. Not only we give some characterizations of fuzzy obstinate ideals, but also bring the extension theorem of fuzzy obstinate ideal of an MV -algebra A. We investigate the relationships between fuzzy obstinate ideals and the other fuzzy ideals of an MV -algebra. We ...
متن کامل