The PageRank algorithm has famously been used by Google to rank web pages by assigning a reputation which is based on the quantity and quality of links to said web page. The underlying process in ranking the web pages is solving an eigenvalue problem with a Markov matrix.

Given the physical problem, there is belief that knowledge of the Markov structure and the sparsity of the matrix can be exploited with hopes to accelerate the convergence of the eigenvalues. Research into the structure of the Markov chain structure will be conducted with particular attention to properties which can lead to hyper-tuning the parameters for the eigenvalue problem. Sep Kamvar’s “Numerical Algorithms for Personalized Search in Self-organizing Information Networks” will be read to develop an understanding of the PageRank problem as well as develop intuition. Beyond this, modern methods for accelerating acceleration will be tested both parameterized independently of Markov chain properties and dependently on Markov structure.

As the world-wide-web continues to expand in size and importance, the importance for an accelerated convergence cannot be easily overlooked. The effects of a small increase can translate to a massive difference when the sheer scale of web users is taken into consideration.