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algebra class. Both advise the computational approaches to digital steward- ship group at Stanford, which has funded part of my research. I’m grateful for their involvement in my research and general education at Stanford. And then there’s Paul. For those reading this who don’t know, Paul Con- stantine was a fellow Ph.D. student at Stanford. Over a fateful beer, we realized that the random alpha PageRank ideas in chapter 4 are possible and make sense. Subsequently, this research blossomed into almost two theses: his thesis on parameterized matrix equations and mine on PageRank. It’s been a wonderful collaboration, and this thesis would be rather different without these pieces. During my research, I’ve had three mentors: Leonid Zhukov, Gene H. Golub, and Michael Saunders. Leonid was my first academic mentor, although he was officially my men- tor as an intern at Overture and Yahoo!. He never seemed to quite agree with my philosophy on ordering authors (I try to use alphabetical ordering) and kept claiming that I was making him “less important” on papers (we all know where Z lies in the alphabet). In this case, he’s first because the order is chronological. Leonid patiently set me straight on matters of matrix computations. He took me through latent semantic indexing (LSI), principle component analysis (PCA), PageRank (well, he started me on PageRank), spectral clustering, semi-definite programming, and visualization, all with explanations that were clear, correct, and physically motivated. I’m indebted to him for this introduction. Gene H. Golub was my first Ph.D. adviser. He opened doors for me during my stint as his student. Our initial work on a least squares problem never went anywhere useful. But we soared with PageRank—literally, in fact. Gene’s stature ensured I could attend a workshop on linear algebra for the web at Schloss Dagstuhl in Germany. With a few small exceptions, everyone working on PageRank was there. It was a tremendous opportunity to learn about PageRank from the experts. Later, Gene helped me arrange a visit to the numerical analysis group at Oxford while he was on his sabbatical there. Gene was famous for claiming that becoming his student was a lifetime commitment. He died shortly into my fourth year. I’m still saddened that my tenure under him was so short. I believe he would have loved the interplay between PageRank and quadrature that developed in chapter 4. He was a great adviser. xiPDF Image | Instagram Cheat Sheet
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