Related papers: Recursive calculation of matrix elements for the g…
We develop a recursive computational procedure to efficiently calculate the macroscopic dielectric function of multi-component metamaterials of arbitrary geometry and composition within the long wavelength approximation. Although the…
The report is devoted to the concept of creating block-recursive matrix algorithms for computing on a supercomputer with distributed memory and dynamic decentralized control.
We give an overview of the theoretical results for matrix block-recursive algorithms in commutative domains and present the results of experiments that we conducted with new parallel programs based on these algorithms on a supercomputer…
In kernel methods, temporal information on the data is commonly included by using time-delayed embeddings as inputs. Recently, an alternative formulation was proposed by defining a gamma-filter explicitly in a reproducing kernel Hilbert…
A matrix balanced version of the Recursive Centered T Matrix Algorithm (RCTMA) applicable to systems possessing resonant inter-particle couplings is presented. Possible domains of application include systems containing interacting localized…
We develop a unified method to study spectral determinants for several different manifolds, including spheres and hemispheres, and projective spaces. This is a direct consequence of an approach based on deriving recursion relations for the…
Electronic structure methods that exploit nonorthogonal Slater determinants face the challenge of efficiently computing nonorthogonal matrix elements. In a recent publication, H. G. A. Burton, J. Chem. Phys. 154, 144109 (2021), I introduced…
A general method is described for finding algebraic expressions for matrix elements of any one- and two-particle operator for an arbitrary number of subshells in an atomic configuration, requiring neither coefficients of fractional…
We consider estimation procedures which are recursive in the sense that each successive estimator is obtained from the previous one by a simple adjustment. We study rate of convergence of recursive estimation procedures for the general…
A recursion formula is derived which allows to evaluate invariant integrals over the orthogonal group O(N), where the integrand is an arbitrary finite monomial in the matrix elements of the group. The value of such an integral is…
Formulas are presented for the recursive generation of four-body integrals in which the integrand consists of arbitrary integer powers (>= -1) of all the interparticle distances r_ij, multiplied by an exponential containing an arbitrary…
We present a novel construction of recursion operators for scalar second-order integrable multidimensional PDEs with isospectral Lax pairs written in terms of first-order scalar differential operators. Our approach is quite straightforward…
This paper presents a regularized recursive identification algorithm with simultaneous on-line estimation of both the model parameters and the algorithms hyperparameters. A new kernel is proposed to facilitate the algorithm development. The…
In this paper, we describe a reliable symbolic computational algorithm for inverting general cyclic heptadiagonal matrices by using parallel computing along with recursion. The algorithm is implementable to the Computer Algebra System(CAS)…
General method is suggested to find non-relativistic and relativistic matrix elements of one- and two-electron operators for any number of open shells in atom, requiring neither coefficients of fractional parentage nor unit tensors. It is…
We present a novel class of methods to compute functions of matrices or their action on vectors that are suitable for parallel programming. Solving appropriate simple linear systems of equations in parallel (or computing the inverse of…
A new runtime environment for the execution of recursive matrix algorithms on a supercomputer with distributed memory is proposed. It is designed both for dense and sparse matrices. The environment ensures decentralized control of the…
In this paper we analyse Cline's matrix equation, generalized Penrose's matrix system and a matrix system for k-commutative {1}-inverses. We determine reproductive and non-reproductive general solutions of analysed matrix equation and…
Thomas-Fermi theory is developed to evaluate nuclear matrix elements averaged on the energy shell, on the basis of independent particle Hamiltonians. One- and two-body matrix elements are compared with the quantal results and it is…
We consider equations arising from rational Lax representations. A general method to construct recursion operators for such equations is given. Several examples are given, including a degenerate bi-Hamiltonian system with a recursion…