The problem of reducing the fragility of digital controllers and filters implemented using finite-precision, floating-point arithmetic is considered. Floating-point arithmetic parameter uncertainty is multiplicative, unlike parameter uncertainty resulting from fixedpoint arithmetic. Based on first-order eigenvalue sensitivity analysis, an upper bound on the eigenvalue perturbations is derived. ...

We consider discrete time linear population models of the form n(t+1)=An(t) where A is a population projection matrix or integral projection operator, and n(t) represents a structured population at time t. It is well known that the asymptotic growth or decay rate of n(t) is determined by the leading eigenvalue of A. In practice, population models have substantial parameter uncertainty, and it m...

In this paper, we study the robust Rayleigh quotient optimization problems that arise when optimizing in worst-case the Rayleigh quotient of data matrices subject to uncertainties. We propose to solve such problem by exploiting its characterization as a nonlinear eigenvalue problem with eigenvector nonlinearity. With this approach, we can show that a commonly used iterative method can be diverg...

We introduce a new method for the calculation of bounds on the eigenvalues of Hessian matrices of twice continuously differentiable functions. Eigenvalue bounds of Hessian matrices arise in a number of notoriously difficult tasks in computational chemical engineering. For example, Hessian matrix eigenvalue bounds are used in global nonlinear optimization, global convexity/concavity analysis in ...

The convergence analysis of iterative methods for nonlinear eigenvalue problems is in the most cases restricted either to algebraic simple eigenvalues or to polynomial eigenvalue problems. In this paper we consider two classical methods for general holomorphic eigenvalue problems, namely the nonlinear generalized Rayleigh quotient iteration (NGRQI) and the augmented Newton method. For both meth...

A chemical reaction network can admit multiple positive steady states if and only if there exists a positive steady state having a zero eigenvalue with its eigenvector in the stoichiometric subspace. A zero eigenvalue analysis is proposed which provides a necessary and sufficient condition to determine the possibility of the existence of such a steady state. The condition forms a system of ineq...

In the 1960s, Atkinson introduced an abstract algebraic setting for multiparameter eigenvalue problems. He showed that a nonsingular multiparameter eigenvalue problem is equivalent to the associated system of generalized eigenvalue problems. Many theoretical results and numerical methods for nonsingular multiparameter eigenvalue problems are based on this relation. In this paper, the above rela...

This article deals with the free in-plane vibration analysis of a frame with four arbitrary inclined members by differential transform method. Based on four differential equations and sixteen boundary and compatibility conditions, the related structural eigenvalue problem will be analytically formulated. The frequency parameters and mode shapes of the frame will be calculated for various values...