Related papers: On the Recurrence Formula for Fixed Points of the …

We present for the first time an explicit, complete and closed-form solution to the three-dimensional problem of two fixed centres, based on Weierstrass elliptic and related functions. With respect to previous treatments of the problem, our…

We present a finite-order system of recurrence relations for a permanent of circulant matrices containing a band of k any-value diagonals on top of a uniform matrix (for k = 1, 2, and 3) as well as the method for deriving such recurrence…

We consider a variation of the classical proximal-gradient algorithm for the iterative minimization of a cost function consisting of a sum of two terms, one smooth and the other prox-simple, and whose relative weight is determined by a…

Recursive formulas are derived for the number of solutions of linear and quadratic Diophantine equations with positive coefficients. This result is further extended to general non-linear additive Diophantine equations. It is shown that all…

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…

We call $i$ a fixed point of a given sequence if the value of that sequence at the $i$-th position coincides with $i$. Here, we enumerate fixed points in the class of restricted growth sequences. The counting process is conducted by…

We describe a procedure based on the iteration of an initial function by an appropriated operator, acting on continuous functions, in order to get a fixed point. This fixed point will be a calibrated subaction for the doubling map on the…

We derive a concise closed-form solution for a linear three-term recurrence relation. Such recurrence relations are very common in the quantitative sciences, and describe finite difference schemes, solutions to problems in Markov processes…

This paper revisits the well-studied fixed point problem from a unified viewpoint of mathematical modeling and canonical duality theory, i.e. the original problem is first reformulated as a nonconvex optimization problem, its well-posedness…

In this paper we propose a stochastic primal dual fixed point method (SPDFP) for solving the sum of two proper lower semi-continuous convex function and one of which is composite. The method is based on the primal dual fixed point method…

In this paper we give efficient algorithms for computing second-, third-, and fourth-order linear recurrences. We also present an algorithm scheme for computing terms with the indices $N,\ldots,N+n-1$ of an $n$th-order linear recurrence.…

Characteristic points have been a primary tool in the study of a generating function defined by a single recursive equation. We investigate the proper way to adapt this tool when working with multi-equation recursive systems.

We describe a simple method that produces automatically closed forms for the coefficients of continued fractions expansions of a large number of special functions. The function is specified by a non-linear differential equation and initial…

In a previous work, we developed an algorithm for the computation of incomplete Bessel functions, which pose as a numerical challenge, based on the $G_{n}^{(1)}$ transformation and Slevinsky-Safouhi formula for differentiation. In the…

We study the convergence of random function iterations for finding an invariant measure of the corresponding Markov operator. We call the problem of finding such an invariant measure the stochastic fixed point problem. This generalizes…

We present a constructive proof of Brouwer's fixed point theorem for uniformly continuous and sequentially locally non-constant functions based on the existence of approximate fixed points. And we will show that Brouwer's fixed point…

We prove recursive formulas for sums of squares and sums of triangular numbers in terms of sums of divisors functions and we give a variety of consequences of these formulas. Intermediate applications include statements about positivity of…

Well-founded fixed points have been used in several areas of knowledge representation and reasoning and to give semantics to logic programs involving negation. They are an important ingredient of approximation fixed point theory. We study…

We construct fast algorithms for evaluating transforms associated with families of functions which satisfy recurrence relations. These include algorithms both for computing the coefficients in linear combinations of the functions, given the…

Specification languages are essential in deductive program verification, but they are usually based on first-order logic, hence less expressive than the programs they specify. Recently, trace specification logics with fixed points that are…