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We study the problem of estimating precision matrices in Gaussian distributions that are multivariate totally positive of order two ($\mathrm{MTP}_2$). The precision matrix in such a distribution is an M-matrix. This problem can be…
A new procedure is developed which enables one to start from the quark and lepton mass and mixing data at the low scale and construct mass matrices which exhibit simple SO(10) structure at the SUSY GUT scale. This approach is applied to the…
Partition of unity methods, such as the extended finite element method (XFEM) allow discontinuities to be simulated independently of the mesh [1]. This eliminates the need for the mesh to be aligned with the discontinuity or cumbersome…
Many authors have studied the numerical computation of conformal mappings (numerical conformal mapping), and there are nowadays several efficient numerical schemes. Among them, Amano's method offers a straightforward numerical procedure for…
Schemes for exact multiplication of small matrices have a large symmetry group. This group defines an equivalence relation on the set of multiplication schemes. There are algorithms to decide whether two schemes are equivalent. However, for…
The weighted star discrepancy is a quantitative measure for the performance of point sets in quasi-Monte Carlo algorithms for numerical integration. We consider polynomial lattice point sets, whose generating vectors can be obtained by a…
An integral equation based scheme is presented for the fast and accurate computation of effective conductivities of two-component checkerboard-like composites with complicated unit cells at very high contrast ratios. The scheme extends…
The last decade has witnessed the emergence of magneto-active polymers (MAPs) as one of the most advanced multi-functional soft composites. Depending on the magnetisation mechanisms and responsive behaviour, MAPs are mainly classified into…
The algorithm for finding the optimal consistent approximation of an inconsistent pairwise comparisons matrix is based on a logarithmic transformation of a pairwise comparisons matrix into a vector space with the Euclidean metric.…
An explicit second-order numerical method to integrate the isokinetic equations of motion is derived by fitting circular arcs through every three consecutive points of the discretized trajectory, so that the tangent and the curvature…
This article presents an innovative methodology for locating injection points in injection-molded parts using intelligent models with geometric algorithms for discrete topologies. The first algorithm calculates the center of mass of the…
We study schemes for interpolating functions that take values in the special orthogonal group $SO(n)$. Our focus is on interpolation schemes obtained by embedding $SO(n)$ in a linear space, interpolating in the linear space, and mapping the…
The purely numerical evaluation of multi-loop integrals and amplitudes can be a viable alternative to analytic approaches, in particular in the presence of several mass scales, provided sufficient accuracy can be achieved in an acceptable…
We describe a dynamic programming algorithm for exact counting and exact uniform sampling of matrices with specified row and column sums. The algorithm runs in polynomial time when the column sums are bounded. Binary or non-negative integer…
The finite element method (FEM) has several computational steps to numerically solve a particular problem, to which many efforts have been directed to accelerate the solution stage of the linear system of equations. However, the finite…
In various areas of applied numerics, the problem of calculating the logarithm of a matrix A emerges. Since series expansions of the logarithm usually do not converge well for matrices far away from the identity, the standard numerical…
In this paper, we consider parametric ideals and introduce a notion of comprehensive involutive system. This notion plays the same role in theory of involutive bases as the notion of comprehensive Groebner system in theory of Groebner…
A method used previously to calculate the masses of the vector mesons is extended to the calculation of the nucleon resonances. The method is based on the choice of integration kernels which eliminate the unknown parts of the spectrum. We…
This paper is devoted to studying the global and finite convergence of the semi-smooth Newton method for solving a piecewise linear system that arises in cone-constrained quadratic programming problems and absolute value equations. We first…
A special purpose solver, based on the Magnus expansion, well suited for the integration of the linear three neutrino oscillations equations in matter is proposed. The computations are speeded up to two orders of magnitude with respect to a…