Mathematical Software
We describe a new data format for storing triangular, symmetric, and Hermitian matrices called RFPF (Rectangular Full Packed Format). The standard two dimensional arrays of Fortran and C (also known as full format) that are used to…
We present a method of computing with matrices over very small finite fields of size larger than 2. Specifically, we show how the Method of Four Russians can be efficiently adapted to these larger fields, and introduce a row-wise matrix…
The notion of complex systems is common to many domains, from Biology to Economy, Computer Science, Physics, etc. Often, these systems are made of sets of entities moving in an evolving environment. One of their major characteristics is the…
A method for solving cyclic block three-diagonal systems of equations is generalized for solving a block cyclic penta-diagonal system of equations. Introducing a special form of two new variables the original system is split into three…
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…
Starting from the basic ideas of mathematica, we give a detailed description about the way of linking of external programs with mathematica through proper mathlink commands. This article may be quite helpful for the beginners to start with…
Mathematica is a versatile equipment for doing numeric and symbolic computations and it has wide spread applications in all branches of science. Mathematica has a complete consistency to design it at every stage that gives it multilevel…
The paper is organized as a self-contained literate Haskell program that implements elements of an executable finite set theory with focus on combinatorial generation and arithmetic encodings. The code, tested under GHC 6.6.1, is available…
As multicore systems continue to gain ground in the High Performance Computing world, linear algebra algorithms have to be reformulated or new algorithms have to be developed in order to take advantage of the architectural features on these…
We present a systematic, algebraically based, design methodology for efficient implementation of computer programs optimized over multiple levels of the processor/memory and network hierarchy. Using a common formalism to describe the…
The ocean general circulation model OPA is developed by the LODYC team at Paris VI university. OPA has recently undergone a major rewriting, migrating to FORTRAN95, and its adjoint code needs to be rebuilt. For earlier versions, the adjoint…
Cody & Waite argument reduction technique works perfectly for reasonably large arguments but as the input grows there are no bit left to approximate the constant with enough accuracy. Under mild assumptions, we show that the result computed…
Real number calculations on elementary functions are remarkably difficult to handle in mechanical proofs. In this paper, we show how these calculations can be performed within a theorem prover or proof assistant in a convenient and highly…
This brief paper: (1) Discusses strategies to generate random test cases that can be used to extensively test any Linear Distance Program (LDP) software. (2) Gives three numerical examples of input cases generated by this strategy that…
Gappa uses interval arithmetic to certify bounds on mathematical expressions that involve rounded as well as exact operators. Gappa generates a theorem with its proof for each bound treated. The proof can be checked with a higher order…
We construct an algorithm for implementing the discrete wavelet transform by means of matrices in SO_2(R) for orthonormal compactly supported wavelets and matrices in SL_m(R), m > = 2, for compactly supported biorthogonal wavelets. We show…
A novel parallel algorithm for matrix multiplication is presented. The hyper-systolic algorithm makes use of a one-dimensional processor abstraction. The procedure can be implemented on all types of parallel systems. It can handle…
The rapid and widespread adoption of Java has created a demand for reliable and reusable mathematical software components to support the growing number of compute-intensive applications now under development, particularly in science and…
The basic statistical methods of data representation did not change since their emergence. Their simplicity was dictated by the intricacies of computations in the before computers epoch. It turns out that such approach is not uniquely…
Since its inception as a student project in 2001, initially just for the handling (as the name implies) of convex polyhedra, the Parma Polyhedra Library has been continuously improved and extended by joining scrupulous research on the…