The mathematical theory of Krylov subspace methods with a focus on solving systems of linear algebraic equations is given a detailed treatment in this principles-based book. Starting from the idea of projections, Krylov subspace methods are characterised by their orthogonality and minimisation properties. Projections onto highly nonlinear Krylov subspaces… (More)
We introduce a method to determine the retinal nerve fiber layer (RNFL) thickness in OCT images based on anisotropic noise suppression and deformable splines. Spectral-Domain Optical Coherence Tomography (SDOCT) data was acquired at 29 kHz A-line rate with a depth resolution of 2.6 μm and a depth range of 1.6 mm. Areas of 9.6x6.4 mm 2 and 6.4x6.4 mm 2 were… (More)
Grady for their support and the opportunity to work on this project and Dr. Bradley Vander Zanden for serving on my thesis committee. I thank Dr. George Ostrouchov for his advice on the statistical aspect of the project. Abstract Data Mining is the application of algorithms for extracting valuable information from large databases in order to make important… (More)
A polylogarithmic bound for an iterative substructuring method for spectral elements in three dimensions, SIAM J. Numer. An optimal preconditioner for a class of saddle point problems with a penalty term, Tech. Howard Elman and Axel Klawonn for many helpful discussions and suggestions.
We have divided this book into five main chapters. Chapter 1 gives the motivation for this book and the use of templates. Chapter 2 describes stationary and nonstationary iterative methods. In this chapter we present both historical development and state-of-the-art methods for solving some of the most challenging computational problems facing researchers.… (More)
5365 Moreover, GMRES-RP is the most efficient, and CGS-RP is the least efficient. ACKNOWLEDGMENT The authors are grateful to the anonymous reviewers for their helpful reviews and suggestions, and would like to thank Y. Wang for the assistance in preparing some of the numerical results. A robust preconditioned GMRES method for electromagnetic scattering from… (More)