Related papers: Explicit Inversions of Certain Matrices I
We solve the difference equation with linear coefficients by the Momentenansatz to obtain explicit formulas for orthogonal polynomials.
We present explicit formulas for Moore-Penrose inverses of some families of set inclusion matrices arising from sets, vector spaces, and designs.
In this work we deduce explicit formulae for the elements of the matrices that represent the action of integro-differential operators over the coefficients of generalized Fourier series. Our formulae are obtained by performing operations on…
Matrices resulting from the discretization of a kernel function, e.g., in the context of integral equations or sampling probability distributions, can frequently be approximated by interpolation. In order to improve the efficiency, a…
This paper presents an iterative method suitable for inverting semilinear problems which are important kernels in many numerical applications. The primary idea is to employ a parametrization that is able to reduce semilinear problems into…
Generalizations and variations of the fundamental lemma by Willems et al. are an active topic of recent research. In this note, we explore and formalize the links between kernel regression and some known nonlinear extensions of the…
We present explicit inverses of two Brownian--type matrices, which are defined as Hadamard products of certain already known matrices. The matrices under consideration are defined by $3n-1$ parameters and their lower Hessenberg form…
Discrete orthogonal matrices have several applications in information technology, such as in coding and cryptography. It is often challenging to generate discrete orthogonal matrices. A common approach widely in use is to discretize…
We give a formula for the inverse matrix to an infinite matrix with possibly noncommutative entries, generalizing the Newton interpolation formula and the Taylor formula.
Orthogonal polynomials and multiple orthogonal polynomials are interesting special functions because there is a beautiful theory for them, with many examples and useful applications in mathematical physics, numerical analysis, statistics…
Specific definitions of the core and core-EP inverses of complex tensors are introduced. Some characterizations, representations and properties of the core and core-EP inverses are investigated. The results are verified using specific…
We prove Horrocks' theorem for the odd elementary orthogonal group, which gives a decomposition of an orthogonal matrix with entries from a polynomial ring $R[X]$, over a commutative ring $R$ in which 2 is invertible, as a product of an…
The inverse problem which arises in the Camassa--Holm equation is revisited for the class of discrete densities. The method of solution relies on the use of orthogonal polynomials. The explicit formulas are obtained directly from the…
Highly localized kernels based on orthogonal polynomials have been studied and utilized over several regular domains. Much of the results deduced via these kernels can be treated uniformly in the framework of localizable spaces of…
We study compositional inverses of permutation polynomials, complete mappings, mutually orthogonal Latin squares, and bent vectorial functions. Recently it was obtained in [33] the compositional inverses of linearized permutation binomials…
Inverse Vandermonde matrix calculation is a long-standing problem to solve nonsingular linear system $Vc=b$ where the rows of a square matrix $V$ are constructed by progression of the power polynomials. It has many applications in…
The Hankel determinant representations for the partition function and boundary correlation functions of the six-vertex model with domain wall boundary conditions are investigated by the methods of orthogonal polynomial theory. For specific…
We give a new and simple proof of the Hankel inversion formula for the classical Hankel transform which holds for a complex order with real part greater than -1. Using the proof of this formula we obtain the full description of the Kirillov…
This brief note concerns the invertibility of certain alternant matrices. In particular those that consisting of polynomials and products of polynomials and logarithms are shown to be invertible under appropriate conditions on the degrees…
We give an explicit Pieri formula for Macdonald polynomials attached to the root system C_n (with equal multiplicities). By inversion we obtain an explicit expansion for two-row Macdonald polynomials of type C.