Related papers: Minimal Polynomial Algorithms for Finite Sequences
We use discrete holomorphic polynomials to prove that, given a refining sequence of critical maps of a Riemann surface, any holomorphic function can be approximated by a converging sequence of discrete holomorphic functions.
This paper presents a new derivative parsing algorithm for parsing expression grammars; this new algorithm is both simpler and faster than the existing parsing expression derivative algorithm presented by Moss. This new algorithm improves…
We show how to reduce a general, strictly-feasible LP problem, into a min-max problem, which can be solved by the algorithm from the third section of my thesis.
We re-examine previous constructions of infinite binary words containing few distinct squares with the goal of finding the "simplest", in a certain sense. We exhibit several new constructions. Rather than using tedious case-based arguments…
The simplex algorithm is one of the most popular algorithms to solve linear programs (LPs). Starting at an extreme point solution of an LP, it performs a sequence of basis exchanges (called pivots) that allows one to move to a better…
We devise a simple but remarkably accurate iterative routine for calculating the roots of a polynomial of any degree. We demonstrate that our results have significant improvement in accuracy over those obtained by methods used in popular…
We present a lattice algorithm specifically designed for some classical applications of lattice reduction. The applications are for lattice bases with a generalized knapsack-type structure, where the target vectors are boundably short. For…
We obtain a complete classification of minimal simple unitary $W$-algebras.
We detail a simple procedure (easily convertible to an algorithm) for constructing from quasi-uniform samples of $f$ a sequence of linear spline functions converging to the monotone rearrangement of $f$, in the case where $f$ is an almost…
In this paper we consider the minimal polynomial $\psi_n(x)$ of $2\cos (2\pi /n)$. We introduce some polynomial sequences with the same recurrence relation as the rescaled Chebyshev polynomials $t_n(x)=2\, T_n(x/2)$ of the first kind, which…
We give a new fast method for evaluating sprectral approximations of nonlinear polynomial functionals. We prove that the new algorithm is convergent if the functions considered are smooth enough, under a general assumption on the spectral…
The purpose of this article is to present my new proof of the the construction and the convergence theorem of spectral sequences of filtered complexes, which is much shorter and cleaner than the "standard" proof.
We show that a minimal ideal of a finite-dimensional Lie algebra is either simple or abelian.
In this paper, we provide a new scheme for approximating the weakly efficient solution set for a class of vector optimization problems with rational objectives over a feasible set defined by finitely many polynomial inequalities. More…
We propose to classify the power of algorithms by the complexity of the problems that they can be used to solve. Instead of restricting to the problem a particular algorithm was designed to solve explicitly, however, we include problems…
As modeling and visualization applications proliferate, there arises a need to simplify large polygonal models at interactive rates. Unfortunately existing polygon mesh simplification algorithms are not well suited for this task because…
This paper presents an alternative approach to simplify the proofs of some important results related to polynomial mappings in Computational Algebraic Geometry such as Polynomial Implicitization, Image Closure and some properties of the…
In this paper we have considered a finite unitary matrix group with exact elements being unknown and only approximate elements available. Such a group becomes inconsistent with its own multiplication table. We found simple correction…
We derive a simple lower bound for the multi-version coding problem formulated in [1]. We also propose simple algorithms that almost match the lower bound derived. Another lower bound is proven for an extended version of the multi-version…
This paper is a short introduction to orthogonal polynomials, both the general theory and some special classes. It ends with some remarks about the usage of computer algebra for this theory.