Related papers: On pole-swapping algorithms for the eigenvalue pro…
In the space of holomorphic functions in a convex domain it is studied the interpolation problem by means of sums of the series of exponentials converging uniformly on all compact sets of the domain. The discrete set of the interpolation…
Accurate evaluation of nearly singular integrals plays an important role in many boundary integral equation based numerical methods. In this paper, we propose a variant of singularity swapping method to accurately evaluate the layer…
In this paper, we use the Poincare separation theorem for estimating the eigenvalues of the fine grid. We propose a randomized version of the algorithm where several different coarse grids are constructed thus leading to more comprehensive…
This article reviews recent advances in convex optimization algorithms for Big Data, which aim to reduce the computational, storage, and communications bottlenecks. We provide an overview of this emerging field, describe contemporary…
It is well known that the repeated square and multiply algorithm is an efficient way of modular exponentiation. The obvious question to ask is if this algorithm has an inverse which would calculate the discrete logarithm efficiently. The…
We describe two main classes of one-sided trigonometric and hyperbolic Jacobi-type algorithms for computing eigenvalues and eigenvectors of Hermitian matrices. These types of algorithms exhibit significant advantages over many other…
The classical eigenvalue assignment problem is revisited in this note. We derive an analytic expression for pole placement which represents a slight generalization of the celebrated Bass-Gura and Ackermann formulae, and also is closely…
The principle underlying this paper is the basic observation that the problem of simultaneously solving a large class of composite monotone inclusions and their duals can be reduced to that of finding a zero of the sum of a maximally…
A method of representation of a solution as segments of the series in powers of the step of the independent variable is expanded for solving complex systems of ordinary differential equations (ODE): the Lorenz system and other systems. A…
The classical alternating minimization (or projection) algorithm has been successful in the context of solving optimization problems over two variables. The iterative nature and simplicity of the algorithm has led to its application to many…
Motivated by a use case in theoretical hadron physics, we revisit an application of a pole-sum fit to dressing functions of a confined quark propagator. More precisely, we investigate approaches to determine the number and positions of the…
Consider a problem where we are given a bipartite graph H with vertices arranged on two horizontal lines in the plane, such that the two sets of vertices placed on the two lines form a bipartition of H. We additionally require that H admits…
In this research, an optimal algorithm for the Collatz conjecture is presented. Properties such as the convergence of the algorithm and an equation that relates the algorithm to the classical Collatz conjecture are obtained. It is validated…
We develop and analyze quadrature blending schemes that minimize the dispersion error of isogeometric analysis up to polynomial order seven with maximum continuity in the span ($C^{p-1}$). The schemes yield two extra orders of convergence…
A new integration technique for multi-loop Feynman integrals, called the matrix method, is developed and then applied to the divergent part of the overlapping two-loop quark self-energy function $\,i\Sigma\,$ in the light- cone gauge. It is…
We discuss the distributed matching scheme in accelerators where control of transverse beam phase space, oscillation, and transport is accomplished by flexible distribution of focusing elements beyond dedicated matching sections. Besides…
We present a new algorithm for solving an eigenvalue problem for a real symmetric arrowhead matrix. The algorithm computes all eigenvalues and all components of the corresponding eigenvectors with high relative accuracy in $O(n^{2})$…
Column-sparse packing problems arise in several contexts in both deterministic and stochastic discrete optimization. We present two unifying ideas, (non-uniform) attenuation and multiple-chance algorithms, to obtain improved approximation…
We describe a novel switching algorithm based on a ``reverse'' Monte Carlo method, in which the potential is stochastically modified before the system configuration is moved. This new algorithm facilitates a generalized formulation of…
A type of parallel augmented subspace scheme for eigenvalue problems is proposed by using coarse space in the multigrid method. With the help of coarse space in multigrid method, solving the eigenvalue problem in the finest space is…