Mathematical Software
We document the MATLAB code used in the following study: Numerical proof of stability of roll waves in the small-amplitude limit for inclined thin film flow.
The real symmetric tridiagonal eigenproblem is of outstanding importance in numerical computations; it arises frequently as part of eigensolvers for standard and generalized dense Hermitian eigenproblems that are based on a reduction to…
Future extreme-scale computer systems may expose silent data corruption (SDC) to applications, in order to save energy or increase performance. However, resilience research struggles to come up with useful abstract programming models for…
While there is no lack of efficient Krylov subspace solvers for Hermitian systems, there are few for complex symmetric, skew symmetric, or skew Hermitian systems, which are increasingly important in modern applications including quantum…
These notes outline a formal method for program verification of numerical computation. It forms the basis of the software package VPC in its initial phase of development. Much of the style of presentation is in the form of notes that…
This article focuses on the application of model development and opening the source code available and implemented by the Free Software and Open Source FLOSS to the instructional and teaching has both mathematics and computer by the…
Principal component analysis (PCA) is a statistical technique commonly used in multivariate data analysis. However, PCA can be difficult to interpret and explain since the principal components (PCs) are linear combinations of the original…
Methods and an algorithm for computing the generalized Marcum $Q-$function ($Q_{\mu}(x,y)$) and the complementary function ($P_{\mu}(x,y)$) are described. These functions appear in problems of different technical and scientific areas such…
The traditional approach to investigating the stability of a physical system is to linearise the equations about a steady base solution, and to examine the eigenvalues of the linearised operator. Over the past several decades, it has been…
In this paper we present a method for matrix inversion based on Cholesky decomposition with reduced number of operations by avoiding computation of intermediate results; further, we use fixed point simulations to compare the numerical…
In this paper we demonstrate a new technique for deriving discrete adjoint and tangent linear models of finite element models. The technique is significantly more efficient and automatic than standard algorithmic differentiation techniques.…
All but a few digital computers used for scientific computations have supported floating-point and digital arithmetic of rather limited numerical precision. The underlying assumptions were that the systems being studied were basically…
In this paper we describe how DUNE, an open source scientific software framework, is developed. Having a sustainable software framework for the solution of partial differential equations is the main driver of DUNE's development. We take a…
We examine residual evaluation, perhaps the most basic operation in numerical simulation. By raising the level of abstraction in this operation, we can eliminate specialized code, enable optimization, and greatly increase the extensibility…
The Trilinos Project is an effort to facilitate the design, development, integration and ongoing support of mathematical software libraries within an object-oriented framework. It is intended for large-scale, complex multiphysics…
We introduce the Declaratron, a system which takes a declarative approach to specifying mathematically based scientific computation. This uses displayable mathematical notation (Content MathML) and is both executable and semantically well…
We assume some standard choices for the branch cuts of a group of functions and consider the problem of then calculating the branch cuts of expressions involving those functions. Typical examples include the addition formulae for inverse…
Mathematical operators whose transformation rules constitute the building blocks of a multi-linear algebra are widely used in physics and engineering applications where they are very often represented as tensors. In the last century, thanks…
Theorema 2.0 stands for a re-design including a complete re-implementation of the Theorema system, which was originally designed, developed, and implemented by Bruno Buchberger and his Theorema group at RISC. In this paper, we present the…
Mathematica offers, by way of the package Combinatorics, many useful functions to work on graphs and ordered structures, but none of these functions was specific enough to meet the needs of our research group. Moreover, the existing…