Stochastic algorithms in linear algebra: beyond the Markov chains and von Neumann-Ulam scheme

Authors:
Karl Sabelfeld
Affiliations:
Institute Comp. Math. & Math. Geoph., Novosibirsk, Russia
Venue:
NMA'10 Proceedings of the 7th international conference on Numerical methods and applications
Year:
2010

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Abstract

Sparsified Randomization Monte Carlo (SRMC) algorithms for solving systems of linear algebraic equations introduced in our previous paper [34] are discussed here in a broader context. In particular, I present new randomized solvers for large systems of linear equations, randomized singular value (SVD) decomposition for large matrices and their use for solving inverse problems, and stochastic simulation of random fields. Stochastic projection methods, which I call here "random row action" algorithms, are extended to problems which involve systems of equations and constrains in the form of systems of linear inequalities.