We have discussed general methods for solving arbitrary equations, and looked at the special class of polynomial equations. A subclass of the latter comprises all the systems of linear equations to which the area of linear algebra is devoted. In fact, many a problem in numerical analysis can be reduced to one of solving a system of linear equations. We already witnessed this in the use of Newto...

RA-, =RA-&), R,-c = RB__c@) (5) These two parametric equations uniquely determine a trajectory which we shall call the BEBO RC. This we compare to the minimum energy path on the appropriate potential energy surface (PES). A good agreement is known to exist for H2 + H PES (see fig. 1 of ref. [3] and ref. [4]) and for H2 + F [4] where the PES of Bender et al. [5] has been used. The aim of this le...

Michael Gil’ Department of Mathematics, Ben Gurion University of the Negev, P.O. Box 653, Beer-Sheva 84105, Israel Correspondence should be addressed to Michael Gil’, [email protected] Received 20 March 2012; Accepted 28 May 2012 Academic Editor: Andrei Volodin Copyright q 2012 Michael Gil’. This is an open access article distributed under the Creative Commons Attribution License, which permit...

We present efficient algorithms for detecting central and mirror symmetry for the case of algebraic curves defined by means of polynomial parametrizations. The algorithms are based on an algebraic relationship between proper parametrizations of a same curve, which leads to a triangular polynomial system that can be solved in a very fast way; in particular, curves parametrized by polynomials of ...

A graph is called (generically) rigid in Rd if, for any choice of sufficiently generic edge lengths, it can be embedded in Rd in a finite number of distinct ways, modulo rigid transformations. Here we deal with the problem of determining the maximum number of planar Euclidean embeddings as a function of the number of the vertices. We obtain polynomial systems which totally capture the structure...

Scalar linear time-varying systems are addressed. In particular, a new factorization method for the associated scalar polynomial system differential operator is presented. It differs from the classical results due to Cauchy and Floquet, in that it is based upon successive Riccati transformations of the Frobenius companion system matrix. As a consequence, the factorization is obtained in terms o...

A second order numerical method for the primitive equations (PEs) of large-scale oceanic flow formulated in mean vorticity is proposed and analyzed, and the full convergence in L2 is established. In the reformulation of the PEs, the prognostic equation for the horizontal velocity is replaced by evolutionary equations for the mean vorticity field and the vertical derivative of the horizontal vel...

When σ is a quasi-definite moment functional with the monic orthogonal polynomial system {Pn(x)}∞n=0, we consider a point masses perturbation τ of σ given by τ := σ+ λ ∑m l=1 ∑ml k=0((−1) ulk/k!)δ (x− cl), where λ, ulk, and cl are constants with ci = cj for i = j. That is, τ is a generalized Uvarov transform of σ satisfying A(x)τ = A(x)σ, where A(x) = ∏m l=1(x− cl) l. We find necessary and suff...