Scaling of Polynomial Eigenvalue Problems

Sammanfattning

Eigenvalue problems are widely used in a variety of fields including quantum mechanics, data science, biology, geology, engineering and many more. It being such a fundamental part in so many areas makes it important to do what we can to ensure stable and accurate calculations as much as possible. With limited computer capacity, we need good methods to improve stability and minimize loss of accuracy. Scaling of eigenvalue problems may be such a method in many cases. In this thesis we begin by explaining what eigenvalue problems are, how they work, and common methods to solve them, mainly linearization. To illustrate and aid in this, we utilize a real world prob lem that was solved by being represented as a quadratic eigenvalue problem (QEP) and solved using such methods. It is referred to as the beam problem and is recurring throughout the text. Later on, we present a scaling method of our own and perform numerical testing to investigate its effectiveness.