Related papers: A systematic approach to computing and indexing th…
Starting with the recursive extended Euclid's algorithm, we apply a systematic approach using matrix notation to transform it into an iterative algorithm. The partial correctness proof derived from the transformation turns out to be very…
We extend the well-known Dumont--Thomas numeration systems to $\mathbb{Z}$ using an approach inspired by the two's complement numeration system. Integers in $\mathbb{Z}$ are canonically represented by a finite word (starting with…
We exhibit a probabilistic algorithm which computes a rational point of an absolutely irreducible variety over a finite field defined by a reduced regular sequence. Its time--space complexity is roughly quadratic in the logarithm of the…
Iterative probabilistic inference, popularly dubbed the soft-iterative paradigm, has found great use in a wide range of communication applications, including turbo decoding and turbo equalization. The classic approach of analyzing the…
We introduce a new method for Estimation of Signal Parameters based on Iterative Rational Approximation (ESPIRA) for sparse exponential sums. Our algorithm uses the AAA algorithm for rational approximation of the discrete Fourier transform…
An efficient and flexible engine for computing fixed points is critical for many practical applications. In this paper, we firstly present a goal-directed fixed point computation strategy in the logic programming paradigm. The strategy…
In recent work, Zeilberger and the author used a functional equations approach for enumerating permutations with r occurrences of the pattern 12...k. In particular, the approach yielded a polynomial-time enumeration algorithm for any fixed…
We introduce a new type of Krasnoselskii's result. Using a simple differentiability condition, we relax the nonexpansive condition in Krasnoselskii's theorem. More clearly, we analyze the convergence of the sequence…
Efficient solvers for tensor eigenvalue problems are important tools for the analysis of higher-order data sets. Here we introduce, analyze and demonstrate an extrapolation method to accelerate the widely used shifted symmetric higher order…
The aim of this paper is to establish some results regarding Infinite Iterated Function Systems with the help of the Tarski-Kantorovitch fixed-point principles for maps on partially ordered sets. To this end we introduce two new classes of…
To efficiently express tensor data using the Tucker format, a critical task is to minimize the multilinear rank such that the model would not be over-flexible and lead to overfitting. Due to the lack of rank minimization tools in tensor,…
Wooley ({\em J. Number Theory}, 1996) gave an elementary proof of a Bezout like theorem allowing one to count the number of isolated integer roots of a system of polynomial equations modulo some prime power. In this article, we adapt the…
To test a possible relation between the topological entropy and the Arnold complexity, and to provide a non trivial example of a rational dynamical zeta function, we introduce a two-parameter family of two-dimensional discrete rational…
We consider the problem of optimizing a multivariate quadratic function where each decision variable is constrained to be a complex $m$'th root of unity. Such problems have applications in signal processing, MIMO detection, and the…
We construct a family of iterations for computing the principal square root of a square matrix $A$ using Zolotarev's rational minimax approximants of the square root function. We show that these rational functions obey a recursion, allowing…
It is well known that a fixed point iteration for solving a linear equation system converges if and only if the spectral radius of the iteration matrix is less than one. A method is presented which guarantees the Fixed Point, even if this…
In this paper, we present a family of three-point with eight-order convergence methods for finding the simple roots of nonlinear equations by suitable approximations and weight function based on Maheshwari method. Per iteration this method…
A quasi-Toeplitz $M$-matrix $A$ is an infinite $M$-matrix that can be written as the sum of a semi-infinite Toeplitz matrix and a correction matrix. This paper is concerned with computing the square root of invertible quasi-Toeplitz…
A zero-finding technique for solving nonlinear equations more efficiently than they usually are with traditional iterative methods in which the order of convergence is improved is presented. The key idea in deriving this procedure is to…
A method is given for finding roots of a one-variable function using Taylor's expansion of that function and fractional derivative calculated at a suitable tangent point without using Newton's method, but is regarded as a variant of Halley…