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Chebyshev interpolation polynomials exhibit the exponential approximation property to analytic functions on a cube. Based on the Chebyshev interpolation polynomial approximation, we propose iterative polynomial approximation algorithms to…
In our quest for the design, the analysis and the implementation of a subdivision algorithm for finding the complex roots of univariate polynomials given by oracles for their evaluation, we present sub-algorithms allowing substantial…
This note gives a simple approach to q-analogues of some results associated with Abel polynomials.
We propose an improved algorithm for finding roots of polynomials over finite fields. This makes possible significant speedup of the decoding process of Bose-Chaudhuri-Hocquenghem, Reed-Solomon, and some other error-correcting codes.
In this paper, we develop a computationally simpler version of the operator count heuristic for a particular class of domains. The contribution of this abstract is threefold, we (1) propose an efficient closed form approximation to the…
Two contributions to the discussion of Fearnhead P. and D. Prangle (2012). Constructing summary statistics for approximate Bayesian computation: Semi-automatic approx- imate Bayesian computation, J. Roy. Statist. Soc. B, 74 (3).
The most popular method for computing the matrix logarithm is a combination of the inverse scaling and squaring method in conjunction with a Pad\'e approximation, sometimes accompanied by the Schur decomposition. The main computational…
We consider problems with multiple linear objectives and linear constraints and use Adjustable Robust Optimization and Polynomial Optimization as tools to approximate the Pareto set with polynomials of arbitrarily large degree. The main…
This survey describes probabilistic algorithms for linear algebra computations, such as factorizing matrices and solving linear systems. It focuses on techniques that have a proven track record for real-world problem instances. The paper…
We present a new data structure to approximate accurately and efficiently a polynomial $f$ of degree $d$ given as a list of coefficients. Its properties allow us to improve the state-of-the-art bounds on the bit complexity for the problems…
This study reexamines diffusive representations for fractional integrals with the goal of pioneering new variants of such representations. These variants aim to offer highly efficient numerical algorithms for the approximate computation of…
We develop a new symbolic-numeric algorithm for the certification of singular isolated points, using their associated local ring structure and certified numerical computations. An improvement of an existing method to compute inverse systems…
Unions of graph multiplier operators are an important class of linear operators for processing signals defined on graphs. We present a novel method to efficiently distribute the application of these operators. The proposed method features…
In this extended abstract we deal with the relations between the numerical/diophantine approximation and the symbolic/algebraic geometry approachs to solving of multivariate diophentine polynomial systems, obtaining several consecuences…
The motivation of this work stems from the numerical approximation of bounded functions by polynomials satisfying the same bounds. The present contribution makes use of the recent algebraic characterization found in [B. Despr\'es, Numer.…
Multi-homogeneous polynomial systems arise in many applications. We provide bit complexity estimates for solving them which, up to a few extra other factors, are quadratic in the number of solutions and linear in the height of the input…
We construct an effective algorithmic method to compute the homological monodromy of a complex polynomial which is tame. As an application we show the existence of conjugated polynomials in a number field which are not topologically…
The complex-step derivative approximation is a numerical differentiation technique that can achieve analytical accuracy, to machine precision, with a single function evaluation. In this letter, the complex-step derivative approximation is…
We give formulas for the number of polynomials over a finite field with given root multiplicities, in particular in cases when the formula is surprisingly simple (a power of q). Besides this concrete interpretation, we also prove an…
In this paper, we propose a carefully optimized "half-gcd" algorithm for polynomials. We achieve a constant speed-up with respect to previous work for the asymptotic time complexity. We also discuss special optimizations that are possible…