A note on Jacobi Being More Accurate Than $QR$

Jacobi's method is more accurate than QR

We show that Jacobi's method (with a proper stopping criterion) computes small eigenvalues of symmetric positive de nite matrices with a uniformly better relative accuracy bound than QR, divide and conquer, traditional bisection, or any algorithm which rst involves tridiagonalizing the matrix. In fact, modulo an assumption based on extensive numerical tests, we show that Jacobi's method is opti...

On a more accurate multiple Hilbert-type inequality

By using Euler-Maclaurin's summation formula and the way of real analysis, a more accurate multipleHilbert-type inequality and the equivalent form are given. We also prove that the same constantfactor in the equivalent inequalities is the best possible.

It's More Than Just Being Connected

A More Accurate Prediction of Liquid Evaporation Flux

In this work, a more accurate prediction of liquid evaporation flux has been achieved. The statistical rate theory approach, which is recently introduced by Ward and Fang and exact estimation of vapor pressure in the layer adjacent to the liquid–vapor interface have  been used for prediction of this flux. Firstly, the existence of an equilibrium layer adjacent to the liquid-vapor interface ...

A Note on Maass-Jacobi Forms

In this paper, we introduce the notion of Maass-Jacobi forms and investigate some properties of these new automorphic forms. We also characterize these automorphic forms in several ways.