Iterative Schemes Involving Several Mutual Contractions

Annealing of Iterative Stochastic Schemes

Annealing of general iterative stochastic schemes is studied by using Wentzell’s large deviation theory. The convergence of this algorithm is shown under some conditions. The closed form of the critical constant is specified in terms of its potential function of the mean model.

Several Series Identities Involving the Catalan Numbers

In the paper, the authors discover several series identities involving the Catalan numbers, the Catalan function, the Riemanian zeta function, and the alternative Hurwitz zeta function.

Statistical Tests Involving Several Independent Gamma Distributions

Multi-Predicate Induction Schemes for Mutual Recursion

Where mutually recursive data types are used in programming languages, etc., mutually recursive functions are usually required. Mutually recursive functions are also quite common for non-mutually recursive types. Reasoning about recursive functions requires some form of mathematical induction but there have been difficulties in adapting induction methods for simple recursion to the mutually rec...

Convergence rate analysis of several splitting schemes

Splitting schemes are a class of powerful algorithms that solve complicated monotone inclusions and convex optimization problems that are built from many simpler pieces. They give rise to algorithms in which the simple pieces of the decomposition are processed individually. This leads to easily implementable and highly parallelizable algorithms, which often obtain nearly state-of-the-art perfor...