Interval Nonlinear Eigenvalue Problems

Abstract

Nonlinear eigenvalue Problems are currently receiving much attention because of its extensive applications in areas such as the dynamic analysis of mechanical systems, acoustics and fluid mechanics etc. These eigenvalue problems arise in various other applications too. Open literatures reveal that nonlinear eigenvalue problems are solved by various methods when the matrices involved are having crisp or exact elements. But in actual practice the elements of the matrices may not be crisp. Those may be uncertain due to error in the experiments or observations etc. As such, in this study we have considered the uncertainty in term of intervals. Accordingly this thesis investigates a new form of interval nonlinear eigenvalue problem using interval computation. Here the degree of above mentioned nonlinear eigenvalue problem is reduced to standard linear eigenvalue problem and the procedure is applied to various example problems including an application problem of structural mechanics. Also data from Harwell-Boeing collection matrix market have been used for investigation of dynamic analysis of structural engineering. Corresponding plots and Tables are given to understand the problem showing the efficacy and powerfulness of the method.