Related papers: Calculating elements of matrix functions using div…
Although being powerful, the differential transform method yet suffers from a drawback which is how to compute the differential transform of nonlinear non-autonomous functions that can limit its applicability. In order to overcome this…
Interferences in multi-path systems for single and multiple particles are theoretically analyzed. A holistic method is presented, which allows to construct the unitary transition matrix describing interferometers for any port number d and…
We obtain simple formulas for the matrix elements of the resolvent operator (the Green's function) in any finite set of square integrable basis. These formulas are suitable for numerical computations whether the basis elements are…
An efficient coordinate-free notation is elucidated for differentiating matrix expressions and other functions between higher-dimensional vector spaces. This method of differentiation is known, but not explained well, in the literature.…
Complex valued systems with an indefinite matrix term arise in important applications such as for certain time-harmonic partial differential equations such as the Maxwell's equation and for the Helmholtz equation. Complex systems with…
Two improvements with respect to previous formulations are presented for the calculation of the partition function $\mathcal{Z}$ of small, isolated and interacting many body systems. By including anharmonicities and employing a variational…
In this paper we describe a method of calculation of master integrals based on the solution of systems of difference equations in one variable. Various explicit examples are given, as well as the generalization to arbitrary diagrams.
We report the production and benchmarking of several refinements of the power method that enable the computation of multiple extremal eigenpairs of very large matrices. In these refinements we used an observation by Booth that has made…
In general, matrix or tensor-valued functions are approximated using the method developed for vector-valued functions by transforming the matrix-valued function into vector form. This paper proposes a tensor-based interpolation method to…
A recently proposed method of calculating scalar two-loop propagator and vertex functions with massive particles is illustrated with simple examples. A double integral representation is derived with the example of a propagator function. An…
The inverse of the Vandermonde and confluent Vandermonde matrices are presented. In the case of the Vandermonde matrix, we present a decomposition in three factors, one of them a diagonal matrix. The evaluation of such inverse matrices is a…
The inverse power method is a numerical algorithm to obtain the eigenvectors of a matrix. In this work, we develop an iteration algorithm, based on the inverse power method, to numerically solve the Schr\"odinger equation that couples an…
Given a set of matrices, modeled as samples of a matrix-valued function, we suggest a method to approximate the underline function using a product approximation operator. This operator extends known approximation methods by exploiting the…
We study algorithms for the fast computation of modular inverses. Newton-Raphson iteration over $p$-adic numbers gives a recurrence relation computing modular inverse modulo $p^m$, that is logarithmic in $m$. We solve the recurrence to…
In this paper we describe a parallel Gaussian elimination algorithm for matrices with entries in a finite field. Unlike previous approaches, our algorithm subdivides a very large input matrix into smaller submatrices by subdividing both…
MQuantum algorithms of matrix operations are of great significance in many fields in science and technology. In this paper, by leveraging multi-qubit Toffoli gates and basic single-qubit operations, the quantum algorithms of matrix…
Efficient matrix determinant calculations have been studied since the 19th century. Computers expand the range of determinants that are practically calculable to include matrices with symbolic entries. However, the fastest determinant…
The role of differential equations in the process of calculating Feynman integrals is reviewed. An example of a diagram is given for which the method of differential equations was introduced, the properties of the inverse-mass-expansion…
In this paper we explore the practical use of the corner transfer matrix and its higher-dimensional generalization, the corner tensor, to develop tensor network algorithms for the classical simulation of quantum lattice systems of infinite…
We consider the quantum Toda chain using the method of separation of variables. We show that the matrix elements of operators in the model are written in terms of finite number of ``deformed Abelian integrals''. The properties of these…