Title

Measure distortion analysis of solvers for linear algebraic equations

Abstract

Consider the canonical problem of solving a linear system Ax=b. Solving this system is in some sense a closed problem with only specialized, domain-specific research being active. We consider a mutation of this where b is not a constant vector but a random variable -- B following a probability measure p. Now a linear solver, can be seen as a transformation that defines a push-forward measure q = #p such that q is the measure associated with x. By working with measures, uncertainty propagation becomes analytically tractable and precludes the use of expensive MC simulations. Furthermore, this opens up a new measure-theoretic paradigm of analyzing numerical algorithms, which generalizes existing analyses while also opening up interesting pseudo-paradoxical properties. The talk presents initial results and poses open questions.