Related papers: A matrix method based on the Fibonacci polynomials…
A novel polynomial expansion method of symmetric Boolean functions is described. The method is efficient for symmetric Boolean function with small set of valued numbers and has the linear complexity for elementary symmetric Boolean…
Analytic interpolation problems with rationality and derivative constraints occur in many applications in systems and control. In this paper we present a new method for the multivariable case, which generalizes our previous results on the…
Functional lifting methods provide a tool for approximating solutions of difficult non-convex problems by embedding them into a larger space. In this work, we investigate a mathematically rigorous formulation based on embedding into the…
We present a new rational approximation algorithm based on the empirical interpolation method for interpolating a family of parametrized functions to rational polynomials with invariant poles, leading to efficient numerical algorithms for…
Matrices can be augmented by adding additional columns such that a partitioning of the matrix in blocks of rows defines mutually orthogonal subspaces. This augmented system can then be solved efficiently by a sum of projections onto these…
The paper addresses linear hyperbolic systems in one space dimension with random field coefficients. In many applications, a low degree of regularity of the paths of the coefficients is required, which is not covered by classical stochastic…
We propose an algorithm for determining the irreducible polynomials over finite fields, based on the use of the companion matrix of polynomials and the generalized Jordan normal form of square matrices.
Generalized matrix Lotka-Volterra lattice equations are obtained in a systematic way from a "master equation" possessing a bicomplex formulation.
In this paper we present an efficient computational and symbolic algorithms for solving a backward pentadiagonal linear systems. The implementation of the algorithms using Computer Algebra Systems (CAS) such as MAPLE, MACSYMA, MATHEMATICA,…
We describe a general operational method that can be used in the analysis of fractional initial and boundary value problems with additional analytic conditions. As an example, we derive analytic solutions of some fractional generalisation…
A new technique is presented to solve a class of linear boundary value problems (BVP). Technique is primarily based on an operational matrix developed from a set of modified Bernoulli polynomials. The new set of polynomials is an…
We construct so called Darboux matrices and fundamental solutions in the important case of the generalised Hamiltonian (or canonical) systems depending rationally on the spectral parameter. A wide class of explicit solutions is obtained in…
In this article we study a generalization of Fibonomials, replacing the Fibonacci sequences by bivariate s-Fibonacci polynomial sequences. We call the obtained objects "Bivariate s-Fibopolynomials".
In this paper, we give two new coding algorithms by means of right circulant matrices with elements generalized Fibonacci and Lucas polynomials. For this purpose, we study basic properties of right circulant matrices using generalized…
A method for computing integrals of polynomial functions on compact symmetric spaces is given. Those integrals are expressed as sums of functions on symmetric groups.
In \cite{Ka}, the authors obtained a method for deriving special matrices, whose powers are related to Fibonacci and Lucas numbers. In the study, it has been developed a method for deriving special matrices of $3\times 3$ dimensions, whose…
The nonlinear inverse problem of exponential data fitting is separable since the fitting function is a linear combination of parameterized exponential functions, thus allowing to solve for the linear coefficients separately from the…
We present an empirical-yet-rigorous approach for solving a wide class of functional equations, thereby automating many results that previously required considerable human ingenuity and human labor.
Article presents the compatibility matrix method and illustrates it with the application to P vs NP problem. The method is a generalization of descriptive geometry: in the method, we draft problems and solve them utilizing the image…
In this article, we construct matrices associated to Pachner $\frac{n-1}{2}$-$\frac{n-1}{2}$ moves for odd $n$ and matrices associated to Pachner $(\frac{n}{2}-1)$-$\frac{n}{2}$ moves for even $n$. The entries of these matrices are rational…