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We give an overview of the theoretical results for matrix block-recursive algorithms in commutative domains and present the results of experiments that we conducted with new parallel programs based on these algorithms on a supercomputer…

In earlier work, we developed a modular approach for automatic complexity analysis of integer programs. However, these integer programs do not allow non-tail recursive calls or subprocedures. In this paper, we consider integer programs with…

Special matrix functions have recently been investigated for regions of convergence, integral representations and the systems of matrix differential equation that these functions satisfy. In this paper, we find the recursion formulas for…

Real world combinatorial optimization problems such as scheduling are typically too complex to solve with exact methods. Additionally, the problems often have to observe vaguely specified constraints of different importance, the available…

Automatic differentiation is a set of techniques to efficiently and accurately compute the derivative of a function represented by a computer program. Existing C++ libraries for automatic differentiation (e.g. Adept, Stan Math Library),…

Object-oriented programming languages such as Java and Objective C have become popular for implementing agent-based and other object-based simulations since objects in those languages can {\em reflect} (i.e. make runtime queries of an…

This paper presents a numerical function optimization framework designed for constrained optimization problems in robotics. The tool is designed with real-time considerations and is suitable for online trajectory and control input…

Range trees are multidimensional binary trees which are used to perform d-dimensional orthogonal range searching. In this technical report we study the implementation issues of range trees with fractional cascading, named layered range…

The automated repair of C++ compilation errors presents a significant challenge, the resolution of which is critical for developer productivity. Progress in this domain is constrained by two primary factors: the scarcity of large-scale,…

This paper provides a general account of the notion of recursive program schemes, studying both uninterpreted and interpreted solutions. It can be regarded as the category-theoretic version of the classical area of algebraic semantics. The…

Linear algebra algorithms often require some sort of iteration or recursion as is illustrated by standard algorithms for Gaussian elimination, matrix inversion, and transitive closure. A key characteristic shared by these algorithms is that…

We present the C++ program library mr that allows us to reliably calculate the values of the running parameters in the Standard Model at high energy scales. The initial conditions are obtained by relating the running parameters in the…

Computational implementations for solving systems of linear equations often rely on a one-size-fits-all approach based on LU decomposition of dense matrices stored in column-major format. Such solvers are typically implemented with the aid…

We describe BayesMix, a C++ library for MCMC posterior simulation for general Bayesian mixture models. The goal of BayesMix is to provide a self-contained ecosystem to perform inference for mixture models to computer scientists,…

Functional programmers have an established tradition of using traversals as a design pattern to work with recursive data structures. The technique is so prolific that a whole host of libraries have been designed to help in the task of…

The efficient solution of large sparse saddle point systems is very important in computational fluid mechanics. The discontinuous Galerkin finite element methods have become increasingly popular for incompressible flow problems but their…

In this study, a recursive solution technique in conjunction with generalized integrating factors is presented and applied to address first and second order linear differential equations. This approach demonstrates practical utility in…

A well-established approach to reasoning about loops during program analysis is to capture the effect of a loop by extracting recurrences from the loop; these express relationships between the values of variables, or program properties such…

A visual programming language uses pictorial tools such as diagrams to represent its structural units and control stream. It is useful for enhancing understanding, maintenance, verification, testing, and parallelism. This paper proposes a…

Complex algebraic calculations can be performed by reconstructing analytic results from numerical evaluations over finite fields. We describe FiniteFlow, a framework for defining and executing numerical algorithms over finite fields and…