1,720,984 research outputs found
Performance analysis of the computation of the Taylor series coefficients as performed in TADIFF
No full textA detailed rounding errors analysis for the computation of Taylor expansion
coefficients of an analytic real function with respect to one variable, as implemented by
TADIFF, a software package written in C++ specialized for computing Taylor expansion coefficients using Algorithmic Differentiation, is performed. The error analysis is carried out in a finite precision arithmetic system satisfying the IEEE standard 754. Furthermore, time and space complexity of such a computation is discussed. Experimental results aimed to validate both the accuracy and the complexity estimates are presented
Mathematical approach to the performance evaluation of three dimensional variational data assimilation
No full textWe analyse and discuss the performance of a decomposition approach introduced for solving large scale Variational Data Assimilation (DD-VAR DA) problems. Our performance analysis uses a set of matrices (decomposition and execution)[9], built to highlight the dependency relationship among component parts of a computational problem and/or among operators of the algorithm that solves the problem [10?], that are the fundamental characteristics of an algorithm. We will show how performance metrics depend on the complexity of the algorithm and on parameters characterizing the structure of the two matrices, like their number of rows and columns. We use a new definition of speed up, involving the scale-up factor which measure the performance gain in terms of time complexity reduction, to describe the non-linear behavior of the performance gain
A Loosely Coordinated Model for Heap-Based Priority Queues in Multicore Environments
No full textHeap-based priority queues are very common dynamical data structures used in several fields, ranging from operating systems to scientific applications. However,
the rise of new multicore CPUs introduced new challenges in the process of design of these data structures: in addition to traditional requirements like correctness and
progress, the scalability is of paramount importance. It is a common opinion that these two demands are partially in conflict each other so that in these computational environments it is necessary to relax the requirements of correctness and linearizability to achieve high performances. In this paper we introduce a loosely coordinated approach for the management of heap based priority queues on multicore CPUs, with the aim to realize a tradeoff between efficiency and sequential correctness. The approach is based on a sharing of information among only a small number of cores, so that to improve performance without completely losing the features of the data structure. The results obtained on a scientific problem show significant benefits both in terms of parallel efficiency, as well as in terms of numerical accuracy
ReLaTIve: an Ansi C software package for the Real Laplace Transform Inversion
No full textsoftware package della libreria NUMERALGO di Numerical Algorith
ReLaTIve. An Ansi C90 software package for the Real Laplace Transform Inversion
No full textA software package for numerical inversion of Laplace transforms
computable everywhere on the real axis is described. Besides the function to invert the user has only to provide the numerical value (even if it is an approximate value) of the abscissa of convergence and the accuracy required for the inverse function
Technical Documentation for L-BFGS for GPU-CUPA. Reference Manual and User Guide
No full textIn this document is described a L-BFGS subroutine for large-scale constrained optimization algorithm implemented in GPU-CUDA. Here is provided a brief description of the L-BFGS algorithm developed and a brief tour around the main steps of the subroutine is provided. Significant efforts have been made to make the subroutine documenting, so this note should be seen as a prelude to looking at the code itself
Algorithm 946. RELIADIFF. An C++ software package for Real Laplace Transform inversion based on Automatic Differentiation
No full textAlgorithm 662 of the ACM TOMS library is a software package, based on the Weeks method, which is used
for calculating function values of the inverse Laplace transform. The software requires transform values
at arbitrary points in the complex plane. We developed a software package, called ReLIADiff, which is a
modification of Algorithm 662 using transform values at arbitrary points on real axis. ReLIADiff, implemented
in C++, relies on TADIFF software package designed for Algorithmic Differentiation. In this article we present
ReLIADiff focusing on its design principles, performance and use
Performance Parameters for Parallel Algorithms in GPU-Enhanced Environments
No full textThis work analyzes the role of graphic processing units
(GPUs) in the framework of traditional parallel architectures
(MIMD, SIMD, . . .) to find some effective parameters
for the prediction of algorithms performance in a GPUenhanced
environment. We consider a medical imaging application,
namely the deconvolution of 3D Fluorescence Microscopy
images, implemented in C with CUDA extension
on a NVIDIA Tesla C1060: describing its design choices
we intend to show how those parameters can affect actual
algorithms performance
Erratum to: ReLaTIve. An Ansi C90 software package for the Real Laplace Transform Inversion
No full textA software package for numerical inversion of Laplace transforms computable everywhere on the real axis is described. Besides the function to invert the user has only to provide the numerical value (even if it is an approximate value) of the abscissa of convergence and the accuracy required for the inverse function. The software provides a controlled accuracy, i.e. it dynamically computes the so-called maximum attainable accuracy such that numerical results are provided within the greatest value between the user’s required accuracy and the maximum attainable accuracy. This is done because the intrinsic ill posedness of the real inversion problem sometime may prevent to reach the desired accuracy. The method implemented is based on a Laguerre polynomial series expansion of the inverse function and belongs to the class of polynomial-type methods of inversion of the Laplace transform, formally characterized as Collocation methods (C-methods)
Quality assurance of Gaver’s formula for multi-precision Laplace transform inversion in real case
No full textWe are concerned with Gaver’s formula, which is at the heart of a numerical algorithm, widely used in scientific and engineering applications, for computing approximations of inverse Laplace transform in multi-precision arithmetic systems. We demonstrate that, once parameters n (i.e. the number of terms of Gaver’s formula) and (i.e. an upper bound on noise on data) are given, then the number of correct significant digits of computed values of the inverse function is bounded above by . In case of noise free data this number is arbitrarily large, as it is bounded below by n. We establish the requirement of the multi-precision system ensuring that the quality of numerical results is fulfilled. Experiments and comparisons validate the effectiveness of such approach
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