数学软件

Numerical continuation methods track a solution path defined by a homotopy. The systems we consider are defined by polynomials in several variables with complex coefficients. For larger dimensions and degrees, the numerical conditioning…

A hierarchy of semidefinite programming (SDP) relaxations approximates the global optimum of polynomial optimization problems of noncommuting variables. Generating the relaxation, however, is a computationally demanding task, and only…

We describe a new implementation of the elementary transcendental functions exp, sin, cos, log and atan for variable precision up to approximately 4096 bits. Compared to the MPFR library, we achieve a maximum speedup ranging from a factor 3…

Polynomial systems occur in many fields of science and engineering. Polynomial homotopy continuation methods apply symbolic-numeric algorithms to solve polynomial systems. We describe the design and implementation of our web interface and…

Direct discretization of continuum kinetic equations, like the Vlasov equation, are under-utilized because the distribution function generally exists in a high-dimensional (>3D) space and computational cost increases geometrically with…

We present a simple to use, yet powerful code package called NLSEmagic to numerically integrate the nonlinear Schr\"odinger equation in one, two, and three dimensions. NLSEmagic is a high-order finite-difference code package which utilizes…

General-purpose multiprocessors (as, in our case, Intel IvyBridge and Intel Haswell) increasingly add GPU computing power to the former multicore architectures. When used for embedded applications (for us, Synthetic aperture radar) with…

Study of general purpose computation by GPU (Graphics Processing Unit) can improve the image processing capability of micro-computer system. This paper studies the parallelism of the different stages of decimation in time radix 2 FFT…

The generic matrix multiply (GEMM) function is the core element of high-performance linear algebra libraries used in many computationally-demanding digital signal processing (DSP) systems. We propose an acceleration technique for GEMM based…

It is our view that the state of the art in constructing a large collection of graph algorithms in terms of linear algebraic operations is mature enough to support the emergence of a standard set of primitive building blocks. This paper is…

The RngStreams software package provides one viable solution to the problem of creating independent random number streams for simulations in parallel processing environments. Techniques are presented for effectively using RngStreams with…

GPTIPS is a free, open source MATLAB based software platform for symbolic data mining (SDM). It uses a multigene variant of the biologically inspired machine learning method of genetic programming (MGGP) as the engine that drives the…

The aim of this paper is to describe a Matlab toolbox, called $\mu$-diff, for modeling and numerically solving two-dimensional complex multiple scattering by a large collection of circular cylinders. The approximation methods in $\mu$-diff…

Designing a scientific software stack to meet the needs of the next-generation of mesh-based simulation demands, not only scalable and efficient mesh and data management on a wide range of platforms, but also an abstraction layer that makes…

On modern architectures, the performance of 32-bit operations is often at least twice as fast as the performance of 64-bit operations. By using a combination of 32-bit and 64-bit floating point arithmetic, the performance of many dense and…

We propose an effective and flexible way to assemble finite element stiffness and mass matrices in MATLAB. We apply this for problems discretized by edge finite elements. Typical edge finite elements are Raviart-Thomas elements used in…

The purpose of this project is to collect symbol information in the Mizar Mathematical Library and manipulate it into practical and organized documentation. Inspired by the MathWiki project and API reference systems for computer programs,…

Polynomial systems occur in many areas of science and engineering. Unlike general nonlinear systems, the algebraic structure enables to compute all solutions of a polynomial system. We describe our massive parallel predictor-corrector…

In this paper we present two different variants of method for symmetric matrix inversion, based on modified Gaussian elimination. Both methods avoid computation of square roots and have a reduced machine time's spending. Further, both of…

Sparse matrix-vector multiplication (SpMV) is a fundamental building block for numerous applications. In this paper, we propose CSR5 (Compressed Sparse Row 5), a new storage format, which offers high-throughput SpMV on various platforms…