Introduction

# Introduction - CS 290N / 219: Sparse Matrix Algorithms CS...

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CS 290N / 219 CS 290N / 219 : Sparse Matrix Algorithms : Sparse Matrix Algorithms John R. Gilbert ( gilbert@cs.ucsb.edu ) www.cs.ucsb.edu/~gilbert/cs290

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Systems of linear equations: Systems of linear equations: Ax = b Ax = b
Systems of linear equations: Ax = b Systems of linear equations: Ax = b Alice is four years older than Bob. In three years, Alice will be twice Bob’s age. How old are Alice and Bob now?

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Link analysis of the web Link analysis of the web Web page = vertex Link = directed edge Link matrix: A ij = 1 if page i links to page j 1 2 3 4 7 6 5 1 5 2 3 4 6 7 1 5 2 3 4 6 7
Web graph: PageRank (Google) Web graph: PageRank (Google) [Brin, Page] Markov process: follow a random link most of the time; otherwise, go to any page at random. Importance = stationary distribution of Markov process. Transition matrix is p*A + (1-p)*ones(size(A)) , scaled so each column sums to 1. Importance of page

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## Introduction - CS 290N / 219: Sparse Matrix Algorithms CS...

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