A Rigorous Numerical Method in Infinite Dimensions

Date Approved For my mother, in loving memory iii ACKNOWLEDGEMENTS The following are examples of the many people whose support has been instrumental in my completing this thesis. Joe, who offered technical, canine, and brotherly support; Becky, my wonderful and crazy sister; Dad, who accepted that in my case math wins out over physics; Mom, my favorite role model and confidante, who explained the differences between a geek, a nerd, and a turkey and helped me to choose the one I want to be • My advisor, Konstantin, who offered the perfect inspirational mix (complete with a theme song) of laid-back attitude, world travel, and excitement about getting to do math nearly every day; GAIO-guy Oliver who not only seemed to have infinite patience in answering technical questions but also helped to set the stage for the appearance of magical results • My thesis committee members L. gave me encouragement and direction, and Andzrej Swiech in particular for pointing out an important statement in this thesis in need of clarification • My thesis support group: Laura and Sean, whose support and understanding helped me to see an end to the stress, paperwork, and formatting (\end{thesis}[now]($please?*)) Finally, I want to thank all of these people and the many more who made this difficult final year a little easier: