## UC Berkeley / Lawrence Berkeley Laboratory

#### Accurate Randomized Algorithms of Numerical Analysis

**Vladimir Rokhlin, Yale University**

##### January 26th, 2011 at 4PM–5PM in 939 Evans Hall [Map]

Randomized algorithms are ubiqutous in computer science and computer
engineering. Many problems that are intractable when viewed deterministically
can be effectively solved with probabilistic techniques. Perhaps the most
important aspect of most randomized procedures in current use is the fact that
they produce the correct result with (practically speaking) 100% reliability,
and with (essentially) machine precision.

Historically, randomized techniques have been less popular in numerical
analysis. Most of them trade accuracy for speed, and in many numerical
environments one does not want to add yet another source of inaccuracy to
the calculation that is already sufficiently inaccurate. One could say
that in numerical analysis probabilistic methods are an approach of last
resort. I will discuss several probabilistic algorithms of numerical linear
algebra that are never less accurate than their deterministic counterparts, and
in fact tend to produce better accuracy. In many situations, the new schemes
have lower CPU time requirements than existing methods, both asymptotically and
in terms of actual timings. I will illustrate the approach with several
numerical examples, and discuss possible extensions.