We propose a method and algorithm for computing the weighted MoorePenrose inverse of one-variable rational matrices. Continuing this idea, we develop an algorithm for computing the weighted Moore-Penrose inverse of one-variable polynomial matrix. These methods and algorithms are generalizations of the method or computing the weighted Moore-Penrose inverse for constant matrices, originated in [2...

In this thesis we develop estimates for volumes of smooth boundary manifolds by deriving explicit relations between a heat flow across the surface and its volume. Applying these estimates together with existing results on randomised volume computation and rates of rapidly mixing chains on convex sets, we are able to derive a randomised algorithm for computing the surface volume of a smooth conv...

We develop a regularization operator based on smoothing on a locally defined length scale. This operator is defined on L and has approximation properties that are given by the local regularity of the function it is applied to and the local length scale. Additionally, the regularized function satisfies inverse estimates commensurate with the approximation orders. By combining this operator with ...