Related papers: Rational matrix solutions to the Leech equation: T…
This paper contains a re-evaluation of the spectral approach and factorizability for regular matrix polynomials. In addition, solvent theory is extended from the monic and comonic cases to the regular case. The classification of extended…
We reconstruct a rational Lax matrix of size R+1 from its spectral curve (the desingularization of the characteristic polynomial) and some additional data. Using a twisted Cauchy--like kernel (a bi-differential of bi-weight (1-nu,nu)) we…
Given stable rational matrix functions $G$ and $K$, a procedure is presented to compute a stable rational matrix solution $X$ to the Leech problem associated with $G$ and $K$, that is, $G(z)X(z)=K(z)$ and $\sup_{|z|\leq 1}\|X(z)\|\leq 1$.…
Bayesian matrix completion has been studied based on a low-rank matrix factorization formulation with promising results. However, little work has been done on Bayesian matrix completion based on the more direct spectral regularization…
A new method named rational expansion method of exponent function is presented to find exact traveling wave solutions of differential-difference equations. This method generalizes the so-called tanh-method and other similar methods. Some…
We use ring-theoretic methods and methods from the theory of skew braces to produce set-theoretic solutions to the reflection equation. We also use set-theoretic solutions to construct solutions to the parameter-dependent reflection…
This paper proposes an algorithm for computing regularized solutions to linear rational expectations models. The algorithm allows for regularization cross-sectionally as well as across frequencies. A variety of numerical examples illustrate…
In this study, a recursive solution technique in conjunction with generalized integrating factors is presented and applied to address first and second order linear differential equations. This approach demonstrates practical utility in…
The finite Pfaff lattice is given by commuting Lax pairs involving a finite matrix L (zero above the first subdiagonal) and a projection onto Sp(N). The lattice admits solutions such that the entries of the matrix L are rational in the time…
In this paper we consider new regularization methods for linear inverse problems of dynamic type. These methods are based on dynamic programming techniques for linear quadratic optimal control problems. Two different approaches are…
Standard regularization methods that are used to compute solutions to ill-posed inverse problems require knowledge of the forward model. In many real-life applications, the forward model is not known, but training data is readily available.…
Matrix spectral factorization is traditionally described as finding spectral factors having a fixed analytic pole configuration. The classification of spectral factors then involves studying the solutions of a certain algebraic Riccati…
We study a general class of recurrence relations that appear in the application of a matrix diagonalization procedure. We find general closed formula and determine analytical properties of the solutions. We finally apply these findings in…
In this paper an extension of the spectral Lanczos' tau method to systems of nonlinear integro-differential equations is proposed. This extension includes (i) linearization coefficients of orthogonal polynomials products issued from…
A spectral method is developed for the direct solution of linear ordinary differential equations with variable coefficients. The method leads to matrices which are almost banded, and a numerical solver is presented that takes O(m^2n)…
Results on the rational approximation of functions containing singularities are presented. We build further on the ''lightning method'', recently proposed by Trefethen and collaborators, based on exponentially clustering poles close to the…
It is well-known that the two-parameter Mittag-Leffler (ML) function plays a key role in Fractional Calculus. In this paper, we address the problem of computing this function, when its argument is a square matrix. Effective methods for…
We present a complete solution to the so-called tennis ball problem, which is equivalent to counting lattice paths in the plane that use North and East steps and lie between certain boundaries. The solution takes the form of explicit…
This paper provides an efficient recursive approach of the spectral Tau method to approximate the solution of system of generalized Abel-Volterra integral equations. In this regards, we first investigate the existence, uniqueness as well as…
The existence of singularities of the solution for a class of Lax equations is investigated using a development of the fac- torization method first proposed by Semenov-Tian-Shansky and Reymann [11], [9]. It is shown that the existence of a…