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116 5 ⋅ an inner-outer iteration for pagerank summary The inner-outer iteration solves a PageRank problem via a series of Page- Rank problems with smaller values of α. Outer PageRank problems are solved via an inner Richardson iteration. The subsequent algorithm always con- verges for PageRank (theorem 17). In addition, we combine the inner-outer idea with the power method (section 5.5.1), the Gauss-Seidel method (sec- tion 5.5.2), and the BiCG-STAB method (section 5.5.3). All of these ideas reduce the number of matrix-vector products (or an equivalent work metric) required to converge to a PageRank vector for α > 0.85. We also analyze OpenMP shared memory parallelism and provide a conjecture about why the inner-outer iteration is faster (conjecture 18). As a final note, the inner-outer algorithm is low-memory, easy to im- plement, and robust—it has become our PageRank solver of choice when Gauss-Seidel iterations are not practical.PDF Image | MODELS AND ALGORITHMS FOR PAGERANK SENSITIVITY
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