In this thesis, we study the relationship between the generalized eigenvalue problem (GEP) $Ax=\lambda Bx$, and systems of differential equations. We examine both the Jordan canonical form and Kronecker's canonical form (KCF). The first part of this work provides an introduction to the fundamentals of generalized eigenvalue problems and methods for solving this problem. We discuss the QZ algorithm, which can be used to determine the generalized eigenvalues and also how it can be implemented on MATLAB with the built in function 'eig'. One essential facet of this work is the exploration of symmetric matrix pencils, which arise when A and B are both symmetric matrices. Furthermore we discuss discrete velocity models (DVMs) focusing specifically on a 12-velocity model on the plane. The results obtained are then applied to half-space problems for discrete velocity models, with a focus on planar stationary systems.
| Identifer | oai:union.ndltd.org:UPSALLA1/oai:DiVA.org:kau-100047 |
| Date | January 2024 |
| Creators | Esinoye, Hannah Abosede |
| Publisher | Karlstads universitet, Institutionen för matematik och datavetenskap (from 2013) |
| Source Sets | DiVA Archive at Upsalla University |
| Language | English |
| Detected Language | English |
| Type | Student thesis, info:eu-repo/semantics/bachelorThesis, text |
| Format | application/pdf |
| Rights | info:eu-repo/semantics/openAccess |
| Relation | Karlstad University Studies, 1403-8099 |
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