⎯By employing the Lyapunov stability theory and linear matrix inequality (LMI) technique, delaydependent stability criterion is derived to ensure the exponential stability of bi-directional associative memory (BAM) neural networks with time-varying delays. The proposed condition can be checked easily by LMI control toolbox in Matlab. A numerical example is given to demonstrate the effectiveness...

In computer vision, the exponential map is the natural generalisation of the ordinary exponential function to matrix elements. The technique is based on generating a manifold embedding of the geometric features of the scene on which to estimate trajectories primarily of motion or invariance. An advantage of using the exponential map is the existence of a closed form time-update equation for the...

We show that short bounded-depth Frege proofs of matrix identities, such as PQ = I ⊃ QP = I (over the field of two elements), imply short bounded-depth Frege proofs of the pigeonhole principle. Since the latter principle is known to require exponential-size bounded-depth Frege proofs, it follows that the propositional version of the matrix principle also requires bounded-depth Frege proofs of e...

The matrix exponential is a much-studied matrix function having many applications. The Fréchet derivative of the matrix exponential describes the first-order sensitivity of eA to perturbations in A and its norm determines a condition number for eA. Among the numerous methods for computing eA the scaling and squaring method is the most widely used. We show that the implementation of the method i...

After spatial discretization to the fractional diffusion equation by the shifted Grünwald formula, it leads to a system of ordinary differential equations, where the resulting coefficient matrix possesses the Toeplitz-like structure. An exponential quadrature rule is employed to solve such a system of ordinary differential equations. The convergence by the proposed method is theoretically studi...

The matrix exponential plays a fundamental role in linear differential equations arising in engineering, mechanics, and control theory. The most widely used, and the most generally efficient, technique for calculating the matrix exponential is a combination of “scaling and squaring” with a Padé approximation. For alternative scaling and squaring methods based on Taylor series, we present two mo...

SPICE (Simulation Program with Integrated Circuit Emphasis) is a widely used circuit simulation framework for integrated circuit designs. The basic skeleton of SPICE time domain simulation was derived from the versions developed in UC Berkeley during the 1970s. In this paper, we report most recent numerical integration methods to improve traditional SPICE time integration schemes, which are bas...

The evaluation of a matrix exponential function is a classic problem of computational linear algebra. Many different methods have been employed for its numerical evaluation [Moler C and van Loan C 1978 SIAM Review 20 4], none of which produce a definitive algorithm which is broadly applicable and sufficiently accurate, as well as being reasonably fast. Herein, we employ a method which evaulates...

Parabolic partial differential equations with nonlocal boundary specifications feature in the mathematical modeling of many phenomena. In this paper, numerical schemes are developed for obtaining approximate solutions to the initial boundary value problem for one-dimensional diffusion equation with a nonlocal constraint in place of one of the standard boundary conditions. The method of lines (M...