Related papers: A note on algorithmic approach to inverting multiv…
The proof of the theorem concerning to the inverse cyclotomic Discrete Fourier Transform algorithm over finite field is provided.
Models of complex systems are often formalized as sequential software simulators: computationally intensive programs that iteratively build up probable system configurations given parameters and initial conditions. These simulators enable…
In this paper, we introduce new representation and characterization of the weighted core inverse of matrices. Several properties of these inverses and their interconnections with other generalized inverses are also explored. Through…
For formal multivariate power series $\varphi(x)$ an inversion formula of the form $$ \varphi^{-1}(x)=x +\sum_{m=1}^{\infty}\sum_{k=0}^m (-1)^k(m k)\varphi^{\circ k}(x) is offered$$.
We present an algorithmic equivalent statement to the Jacobian conjecture. Given a polynomial map F on an affine space of dimension n, our algorithm constructs n sequences of polynomials such that F is invertible if and only if the zero…
A novel control design approach for general nonlinear systems is described in this paper. The approach is based on the identification of a polynomial model of the system to control and on the on-line inversion of this model. Extensive…
An improved inverse simulated annealing method is presented to determine the structure of complex disordered systems from first principles in agreement with available experimental data or desired predetermined target properties. The…
The author was encouraged to write this review by numerous enquiries from researchers all over the world, who needed a ready-to-use algorithm for the inversion of confluent Vandermonde matrices which works in quadratic time for any values…
In this paper we present a special formula for transforming integrals to series. The resulting series involves binomial transforms with the Taylor coefficients of the integrand. Five applications are provided for evaluating challenging…
In this paper we focus on the solution of shifted quasiseparable systems and of more general parameter dependent matrix equations with quasiseparable representations. We propose an efficient algorithm exploiting the invariance of the…
We first propose a concise singular value decomposition of dual matrices. Then, the randomized version of the decomposition is presented. It can significantly reduce the computational cost while maintaining the similar accuracy. We analyze…
In this paper we propose a new version of differential transform method (we shall call this method as $\alpha$-parameterized differential transform method), which differs from the traditional differential transform method in calculating…
We present a new algorithm to decide isomorphism between finite graded algebras. For a broad class of nilpotent Lie algebras, we demonstrate that it runs in time polynomial in the order of the input algebras. We introduce heuristics that…
We establish a real version of Turrittin's result on polynomial and formal normal forms of linear systems of ODEs with meromorphic coefficients. Both the normal forms or the transformations used have only real coefficients. In order to…
Finding a computationally efficient algorithm for the inverse continuous wavelet transform is a fundamental topic in applications. In this paper, we show the convergence of the inverse wavelet transform.
We recently introduced the notion of an idempotent system. This linear algebraic object is motivated by the structure of an association scheme. There is a type of idempotent system, said to be symmetric. In the present paper we classify up…
In addition to rather complicated general methods it is interesting and valuable to develop fast efficient methods for calculating generators of power integral bases in special types of number fields. We consider sextic fields containing a…
The aim of this paper is to show that there exists a deterministic algorithm that can be applied to compute the factors of a polynomial of degree 2, defined over a finite field, given certain conditions.
We recall first some basic facts on weighted homogeneous functions and filtrations in the ring $A$ of formal power series. We introduce next their analogues for weighted homogeneous diffeomorphisms and vector fields. We show that the Milnor…
We enhance the approximation capabilities of algebraic polynomials by composing them with homeomorphisms. This composition yields families of functions that remain dense in the space of continuous functions, while enabling more accurate…