✦ LIBER ✦

A new approach for finding all zeros for systems of nonlinear functions

✍ Scribed by V.D. Borisevich; V.G. Potemkin; H.G. Wood

Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 308 KB
Volume: 40
Category: Article
ISSN: 0898-1221
DOI: 10.1016/s0898-1221(00)85007-5

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✦ Synopsis

A new concept in calculation techniques for finding all the zeros for a system of equations of nonlinear functions arising in various applications is presented. The concept is based on the following steps. First, the corresponding system of algebraic equations is created as a homomorphical model for an initial system of nonlinear functions. Second, this system is transformed to a Groebner basis. Third, the algebraic equations are solved by means of the original spectral method using constructing a system of spectral problems for rectangular pencils of matrices. In the paper, the computational symbolic-numerical procedure for this approach is described. The results of calculations based on this technique are presented for an application in theoretical analysis of the properties of the impurity-helium metastable phase under super-low temperatures. ~

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