ESTIMATING THE CONDITION NUMBER OF THE FRÉCHET DERIVATIVE OF A MATRIX FUNCTION∗ NICHOLAS J. HIGHAM† AND SAMUEL D. RELTON† Abstract. The Fréchet derivative Lf of a matrix function f : C n×n → Cn×n is used in a variety of applications and several algorithms are available for computing it. We define a condition number for the Fréchet derivative and derive upper and lower bounds for it that differ ...

This paper revisits the problem of stability analyses for neural networks with time-varying delay. A composite-matrix-based integral inequality (CMBII) is presented, which takes delay derivative into account. In this case, coupling information can be fully captured in inequalities derivative. Based on a CMBII, new criterion derived The effectiveness method verified by numerical example.

The Schur--Parlett algorithm, implemented in MATLAB as \textttfunm, evaluates an analytic function $f$ at $n\times n$ matrix argument by using the Schur decomposition and a block recurrence of P...

We discuss conservation laws for gravity theories invariant under general coordinate and local Lorentz transformations. We demonstrate the possibility to formulate these conservation laws in many covariant and noncovariant(ly looking) ways. An interesting mathematical fact underlies such a diversity: there is a certain ambiguity in a definition of the (Lorentz-) covariant generalization of the ...

It has been observed that simultaneous explanation of the solar and atmospheric neutrino deficits and the reported evidence for νμ → νe oscillation from the Los Alamos Liquid Scintillator Detector (LSND) requires at least one extra neutrino species in addition to the three known ones. The extra neutrino must be sterile with respect to the known weak interactions. We present a new mass matrix fo...

The leapfrog scheme is a commonly used second-order method for solving differential equations. Letting Z denote the state of the system, we compute the state at the next time step as Z (t + 1) = H (Z(t);Z(t 1); W), where t denotes a particular time step, H is the nonlinear timestepping operator, and W are parameters that are not time dependent. In this article, we show how the associativity of ...