数学软件
We present a symbolic tool that provides robust algebraic methods to handle automatic deduction tasks for a dynamic geometry construction. The main prototype has been developed as two different worksheets for the open source computer…
Key questions that scientists and engineers typically want to address can be formulated in terms of predictive science. Questions such as: "How well does my computational model represent reality?", "What are the most important parameters in…
An iterative method LSMR is presented for solving linear systems $Ax=b$ and least-squares problem $\min \norm{Ax-b}_2$, with $A$ being sparse or a fast linear operator. LSMR is based on the Golub-Kahan bidiagonalization process. It is…
In this article we discuss the presentation of a random binary matrix using sequence of whole nonnegative numbers. We examine some advantages and disadvantages of this presentation as an alternative of the standard presentation using…
An equivalence relation in the symmetric group, where is a positive integer has been considered. An algorithm for calculation of the number of the equivalence classes by this relation for arbitrary integer has been described.
We describe a new algorithm for Gaussian Elimination suitable for general (unsymmetric and possibly singular) sparse matrices, of any entry type, which has a natural parallel and distributed-memory formulation but degrades gracefully to…
Transforming a matrix over a field to echelon form, or decomposing the matrix as a product of structured matrices that reveal the rank profile, is a fundamental building block of computational exact linear algebra. This paper surveys the…
ProofPeer strives to be a system for cloud-based interactive theorem proving. After illustrating why such a system is needed, the paper presents some of the design challenges that ProofPeer needs to meet to succeed. Contexts are presented…
In order to obtain more accurate solutions of polynomial systems with numerical continuation methods we use multiprecision arithmetic. Our goal is to offset the overhead of double double arithmetic accelerating the path trackers and in…
In this work, we present the M4RIE library which implements efficient algorithms for linear algebra with dense matrices over GF(2^e) for 2 <= 2 <= 10. As the name of the library indicates, it makes heavy use of the M4RI library both…
In this work we describe an efficient implementation of a hierarchy of algorithms for Gaussian elimination upon dense matrices over the field with two elements. We discuss both well-known and new algorithms as well as our implementations in…
We present two add-ons for Mathematica for teaching mathematics to undergraduate and high school students. These two applications, M@th Desktop (MD) and M@th Desktop Tools (MDTools), include several palettes and notebooks covering almost…
The last several years have seen major enhancements to ACL2 functionality, largely driven by requests from its user community, including utilities now in common use such as 'make-event', 'mbe', and trust tags. In this paper we provide…
Many physical, biological or chemical systems are modeled by ordinary differential equations (ODEs) and finding their solution is an every-day-task for many scientists. Here, we introduce a new C++ library dedicated to find numerical…
Computing on graphics processors is maybe one of the most important developments in computational science to happen in decades. Not since the arrival of the Beowulf cluster, which combined open source software with commodity hardware to…
We have developed a parallel algorithm for radial basis function (RBF) interpolation that exhibits O(N) complexity,requires O(N) storage, and scales excellently up to a thousand processes. The algorithm uses a GMRES iterative solver with a…
Vector operations play an important role in high performance computing and are typically provided by highly optimized libraries that implement the BLAS (Basic Linear Algebra Subprograms) interface. In C++ templates and operator overloading…
We present some of the experiments we have performed to best test our design for a library for MathScheme, the mechanized mathematics software system we are building. We wish for our library design to use and reflect, as much as possible,…
In this overview article we present several methods for multiplying matrices and the implementation of these methods in C. Also a little test program is given to compare their running time and the numerical stability. The methods are: naive…
This paper describes a new accumulate-and-add multiplication algorithm. The method partitions one of the operands and re-combines the results of computations done with each of the partitions. The resulting design turns-out to be both…