The usual approach to computing empirical likelihood for the mean uses Newton’s method after eliminating a Lagrange multiplier and replacing the function − log(x) by a quadratic Taylor approximation to the left of 1/n. This paper replaces the quadratic approximation by a quartic. The result is a self-concordant function for which Newton’s method with backtracking has theoretical convergence gua...

We study the consistency of the ladder approximation and the rainbow approximation of the Dyson-Schwinger equation of QCD. By considering the non-Abelian property of QCD, we show that the QED-type Ward-Takahashi identity is not required for the rainbow-ladder approximation of QCD. It indicates that there does not exists any internal inconsistency in the usual rainbow-ladder approximation of QCD...

The a-posteriori error evaluation based on differential approximation of a finite-difference scheme and adjoint equations is addressed. The differential approximation is composed of primal equations and a local truncation error determined by a Taylor series in Largange form. This approach provides the feasibility of both refining the solution and using the Holder inequality for asymptotic bound...

This paper considers two aspects of the nonlinear H∞ control problem: the use of weighting functions for performance and robustness improvement, as in the linear case, and the development of a Galerkin approximation method for the solution of the Hamilton-Jacobi-Isaacs Equation (HJIE) that arises in the output feedback case. Design of nonlinear H∞ controllers obtained by Taylor approximation an...

In this paper, we present random matrix methods for determining the capacity of uncorrelated MIMO channels having partial channel state information, i.e., statistical knowledge of the channel parameters. We show that it is possible to approximate the MIMO channel capacities by Taylor series expansions in order to apply large-scale analysis using random matrix methods. For an adequate approximat...

The a posteriori error evaluation based on differential approximation of a finitedifference scheme and adjoint equations is addressed. The differential approximation is composed of primal equations and a local truncation error determined by a Taylor series in Lagrange form. This approach provides the feasibility of both refining the solution and using the Holder inequality for asymptotic boundi...

Symmetric level-index arithmetic was introduced to overcome the problems of overflow and underflow in the floating-point system. The purpose of this paper is to improve the algorithm performance of SLI arithmetic by introducing an approximation scheme using Taylor’s expansion. Following a brief summary of the SLI system and its algorithm for addition/subtraction, the deduction and analysis of T...

the potential energy surface pes of (h2)2 dimer has been investigated, using five simple rigid rotor models. these models are called: head to head, symmetric side to side, l , steplike and t model. all calculations were done at two levels of ab initio  methods: mp2(full) and qcisd (t,full) using cc-pvtz basis set at singlet state of spin multiplicity. the results of scanning pes were then fitte...