Related papers: Short note on the mass matrix for Gauss-Lobatto gr…
A neutrino mass matrix model M_\nu with M_\nu^T =M_\nu and a model with its inverse matrix form \widetilde{M}_\nu = m_0^2 (M_\nu^*)^{-1} can be diagonalized by the same mixing matrix U_\nu. It is investigated whether a scenario which…
We study left-right symmetric quark mass matrices whose up- and down-sectors have the same structure. This type of realistic mass matrices are derived from orbifold models. We cannot derive some of them by using an extra U(1) symmetry.
Optimality of several quasi-Monte Carlo methods and suboptimality of the sparse-grid quadrature based on the univariate Gauss--Hermite rule is proved in the Sobolev spaces of mixed dominating smoothness of order $\alpha$, where the…
For a given positive random variable $V>0$ and a given $Z\sim N(0,1)$ independent of $V$, we compute the scalar $t_0$ such that the distance between $Z\sqrt{V}$ and $Z\sqrt{t_0}$ in the $L^2(\R)$ sense, is minimal. We also consider the same…
The techniques for polynomial interpolation and Gaussian quadrature are generalized to matrix-valued functions. It is shown how the zeros and rootvectors of matrix orthonormal polynomials can be used to get a quadrature formula with the…
An exact expression for the mass-gap, the ratio of the physical particle mass to the $\Lambda$-parameter, is found for the principal chiral sigma models associated to all the classical Lie algebras. The calculation is based on a comparison…
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…
Gauss-Lobatto quadrature nodes and weights are optimal for closed summation-by-parts (SBP) formulations based on polynomial approximation spaces in the sense that for a prescribed function space they yield an SBP operator of minimal…
A number of applications require the computation of the trace of a matrix that is implicitly available through a function. A common example of a function is the inverse of a large, sparse matrix, which is the focus of this paper. When the…
We analytically compute quadratic mass corrections of order $\alpha_s^3 m_q^2/s$ to the absorptive part of the (non-diagonal) correlator of two axial vector currents. This allows us to find the correction of order $\alpha_s^3 m_q^2/M^2_W$…
We present a framework for accelerating a spectrum of machine learning algorithms that require computation of bilinear inverse forms $u^\top A^{-1}u$, where $A$ is a positive definite matrix and $u$ a given vector. Our framework is built on…
The condition number of a diagonally scaled matrix, for appropriately chosen scaling matrices, is often less than that of the original. Equilibration scales a matrix so that the scaled matrix's row and column norms are equal. Scaling can be…
Bernstein polynomials, long a staple of approximation theory and computational geometry, have also increasingly become of interest in finite element methods. Many fundamental problems in interpolation and approximation give rise to…
A method is introduced for approximate marginal likelihood inference via adaptive Gaussian quadrature in mixed models with a single grouping factor. The core technical contribution is an algorithm for computing the exact gradient of the…
The explicit formula for the elements of the successive intermediate matrices of the Gauss-Jordan elimination procedure for the solution of systems of linear equations is applied to error analysis. Stability conditions in terms of relative…
With the recent experimental advance in our precise knowledge of the neutrino oscillation parameters, the correct form of the 3 X 3 neutrino mass matrix is now approximately known. I discuss how this may be obtained from symmetry…
A precision matrix is the inverse of a covariance matrix. In this paper, we study the problem of estimating the precision matrix with a known graphical structure under high-dimensional settings. We propose a simple estimator of the…
In this paper we present two different variants of method for symmetric matrix inversion, based on modified Gaussian elimination. Both methods avoid computation of square roots and have a reduced machine time's spending. Further, both of…
Calabro et al. (2017) changed the paradigm of the mass and stiffness computation from the traditional element-wise assembly to a row-wise concept, showing that the latter one offers integration that may be orders of magnitude faster.…
Newton's inverse-square law of universal gravitation assumes constant mass. But mass increases with speed and perhaps with gravity. By SR, mass is increased over the rest mass by gamma. Rest mass is here postulated to increase under…