An iterative algorithm for determining a type of solutions of the dispersionful 2-Toda hierarchy characterized by string equations is developed. This type includes the solution which underlies the large-N limit of the Hermitian matrix model in the one-cut case. It is also shown how the double scaling limit can be naturally formulated in this scheme PACS number: 02.30.Ik.

A topological approach of determining the best one out of four solutions of the Hermitian interpolation problem for quintic Pythagorean hodograph curves is presented. An existence theorem is proved together with complete analysis of uniqueness/nonuniqueness properties. A simple formula of obtaining the best solution without using any curve fairing or curvature integral is also presented.

An inversion-free iterative algorithm is presented for solving nonlinear matrix equation with a stepsize parameter t. The existence of the maximal solution is discussed in detail, and the method for finding it is proposed. Finally, two numerical examples are reported that show the efficiency of the method. Keywords—Inversion-free method, Hermitian positive definite

In this paper, we focus on the following coupled linear matrix equations Mi(X,Y ) = Mi1(X) +Mi2(Y ) = Li, with

A new numerical method is developed for solution of the Gel’fand – Levitan – Marchenko inverse scattering integral equations. The method is based on the fast inversion procedure of a Toeplitz Hermitian matrix and special bordering technique. The method is highly competitive with the known discrete layer peeling method in speed and exceeds it noticeably in accuracy at high reflectance.

This paper is devoted to the perturbation analysis for the periodic discrete-time algebraic Riccati equations (P-DAREs). Perturbation bounds and condition numbers of the Hermitian positive semidefinite solution set to the P-DAREs are obtained. The results are illustrated by numerical examples.

ABSTRACT : Quaternion Dirac equation has been obtained from the square root of Klein-Gordon equation in compact and consistent way. Dirac matrices are described as quaternion valued and the Dirac Hamiltonian is considered as Hermitian with real eigenvalues of energy. Dirac spinors and free particle energy solution has been obtained in terms of one component, two-component and four-component Dir...

The paper contains a new non-perturbative representation for subleading contribution to the free energy of multicut solution for hermitian matrix model. This representation is a generalisation of the formula, proposed by Klemm, Marino and Theisen for two cut solution, which was obtained by comparing the cubic matrix model with the topological B-model on the local Calabi-Yau geometry II and was ...

The paper contains a new non-perturbative representation for subleading contribution to the free energy of multicut solution for hermitian matrix model. This representation is a generalisation of the formula, proposed by Klemm, Marino and Theisen for two cut solution, which was obtained by comparing the cubic matrix model with the topological B-model on the local Calabi-Yau geometry II and was ...