Related papers: Explicit formulas for the inverses of Toeplitz mat…
We propose an inertial forward-backward splitting algorithm to compute the zero of a sum of two monotone operators allowing for stochastic errors in the computation of the operators. More precisely, we establish almost sure convergence in…
In this work, new closed-form formulas for the matrix exponential are provided. Our method is direct and elementary, it gives tractable and manageable formulas not current in the extensive literature on this essential subject. Moreover,…
Truncating the Fourier transform averaged by means of a generalized Hausdorff operator, we approximate the adjoint to that Hausdorff operator of the given function. We find the formulas for the rate of approximation in various metrics in…
For statistical inference of means of stationary processes, one needs to estimate their time-average variance constants (TAVC) or long-run variances. For a stationary process, its TAVC is the sum of all its covariances and it is a multiple…
Let $A_\Phi$ be a matrix valued truncated Toeplitz operator-the compression of multiplication operator to vector-valued model space $H^2(E)\ominus \Theta H^2(E)$, where $\Theta$ is a matrix valued non constant inner function. Under…
The large-scale three-dimensional inversion of surface gravity / tensor gravity data is a very challenging numerical and practical problem, which is a highly physical memory usage, time-consuming computation and high precision for…
Based on discrete truncated powers, the beautiful Popoviciu's formulation for restricted integer partition function is generalized. An explicit formulation for two dimensional multivariate truncated power functions is presented. Therefore,…
Algebraic multigrid (AMG) is one of the most efficient iterative methods for solving large sparse system of equations. However, how to build/check restriction and prolongation operators in practical of AMG methods for nonsymmetric {\em…
The nonlocal problems have been used to model very different applied scientific phenomena, which involve the fractional Laplacian when one looks at the L\'{e}vy processes and stochastic interfaces. This paper deals with the nonlocal…
We study a class of rotation invariant determinantal ensembles in the complex plane; examples include the eigenvalues of Gaussian random matrices and the roots of certain families of random polynomials. The main result is a criteria for a…
We study the spectrum of the product of two Toeplitz operators. Assume that the symbols of these operators are continuous and real-valued and that one of them is non-negative. We prove that the spectrum of the product of finite section…
Given a trigonometric polynomial f:[0,1]\to[0,1] of degree m, one can define a corresponding stationary process {X_i}_{i\in Z} via determinants of the Toeplitz matrix for f. We show that for m=1 this process, which is trivially…
In this paper, we present new presentations of group inverse for the sum of two group invertible elements in a Banach algebra. We then apply these results to block complex matrices. The group invertibility of certain block complex matrices…
Approximations by Trefftz functions are rapidly gaining popularity in the numerical solution of boundary value problems of mathematical physics. By definition, these functions satisfy locally, in weak form, the underlying differential…
The need to Fourier transform data sets with irregular sampling is shared by various domains of science. This is the case for example in astronomy or sismology. Iterative methods have been developed that allow to reach approximate…
In recent years more and more involved block structures appeared in the literature in the context of numerical approximations of complex infinite dimensional operators modeling real-world applications. In various settings, thanks the theory…
We study certain linear algebra algorithms for recursive block matrices. This representation has useful practical and theoretical properties. We summarize some previous results for block matrix inversion and present some results on…
We present a new formula for the Drazin inverse of the sum of two complex matrices under weaker conditions with perturbations. By using this additive results, we establish new representations for the Drazin inverse of 2 \times 2 block…
We present a recursive algorithm for multi-coefficient inversion in nonlinear Helmholtz equations with polynomial-type nonlinearities, utilizing the linearized Dirichlet-to-Neumann map as measurement data. To achieve effective recursive…
Radial basis functions provide highly useful and flexible interpolants to multivariate functions. Further, they are beginning to be used in the numerical solution of partial differential equations. Unfortunately, their construction requires…