scholarly journals Correctly rounded exponential function in double-precision arithmetic

2001 ◽  
Author(s):  
David Defour ◽  
Florent de Dinechin ◽  
Jean-Michel Muller
Keyword(s):  
Exponential Function ◽  
Double Precision ◽  
Double Precision Arithmetic

A fast spectral conjugate gradient method for solving nonlinear optimization problems

2021 ◽  
Vol 21 (1) ◽  
pp. 429
Author(s):  
Ali A. Al-Arbo ◽  
Rana Z. Al-Kawaz
Keyword(s):  
Nonlinear Optimization ◽  
Conjugate Gradient ◽  
Optimization Problems ◽  
Double Precision ◽  
Research Issues ◽  
Modified Method ◽  
Fortran Language ◽  
Double Precision Arithmetic ◽  
Spectral Conjugate Gradient ◽  
The Stability

<span>This paper proposes a new spectral conjugate gradient (SCG) approach for solving unregulated nonlinear optimization problems. Our approach proposes Using Wolfe's rapid line scan to adjust the standard conjugate descent (CD) algorithm. A new spectral parameter is a mixture of new gradient and old search path. The path provided by the modified method provides a path of descent for the solution of objective functions. The updated method fits the traditional CD method if the line check is correct. The stability and global convergence properties of the current new SCG are technically obtained from applying certain well-known and recent mild assumptions. We test our approach with eight recently published CD and SCG methods on 55 optimization research issues from the CUTE library. The suggested and all other algorithms included in our experimental research were implemented in FORTRAN language with double precision arithmetic and all experiments were conducted on a PC with 8 GB ram Processor Intel Core i7. The results indicate that our proposed solution outperforms recently reported algorithms by processing and performing fewer iterations in a shorter time.</span>

Three effective inverse Laplace transform algorithms for computing time-domain electromagnetic responses

Geophysics ◽  
2016 ◽  
Vol 81 (2) ◽  
pp. E113-E128 ◽  
Author(s):  
Jianhui Li ◽  
Colin G. Farquharson ◽  
Xiangyun Hu
Keyword(s):  
Laplace Transform ◽  
Frequency Domain ◽  
Time Domain ◽  
Computing Time ◽  
Inverse Laplace Transform ◽  
Double Precision ◽  
Horizontal Electric Dipole ◽  
Time Domain Electromagnetic ◽  
Double Precision Arithmetic ◽  
Efficient Option

The inverse Laplace transform is one of the methods used to obtain time-domain electromagnetic (EM) responses in geophysics. The Gaver-Stehfest algorithm has so far been the most popular technique to compute the Laplace transform in the context of transient electromagnetics. However, the accuracy of the Gaver-Stehfest algorithm, even when using double-precision arithmetic, is relatively low at late times due to round-off errors. To overcome this issue, we have applied variable-precision arithmetic in the MATLAB computing environment to an implementation of the Gaver-Stehfest algorithm. This approach has proved to be effective in terms of improving accuracy, but it is computationally expensive. In addition, the Gaver-Stehfest algorithm is significantly problem dependent. Therefore, we have turned our attention to two other algorithms for computing inverse Laplace transforms, namely, the Euler and Talbot algorithms. Using as examples the responses for central-loop, fixed-loop, and horizontal electric dipole sources for homogeneous and layered mediums, these two algorithms, implemented using normal double-precision arithmetic, have been shown to provide more accurate results and to be less problem dependent than the standard Gaver-Stehfest algorithm. Furthermore, they have the capacity for yielding more accurate time-domain responses than the cosine and sine transforms for which the frequency-domain responses are obtained by interpolation between a limited number of explicitly computed frequency-domain responses. In addition, the Euler and Talbot algorithms have the potential of requiring fewer Laplace- or frequency-domain function evaluations than do the other transform methods commonly used to compute time-domain EM responses, and thus of providing a more efficient option.

Very Fast Tree: speeding up the estimation of phylogenies for large alignments through parallelization and vectorization strategies

2020 ◽  
Vol 36 (17) ◽  
pp. 4658-4659 ◽  
Author(s):  
César Piñeiro ◽  
José M Abuín ◽  
Juan C Pichel
Keyword(s):  
Supplementary Information ◽  
Double Precision ◽  
Supplementary Data ◽  
The Core ◽  
Double Precision Arithmetic

Abstract Motivation FastTree-2 is one of the most successful tools for inferring large phylogenies. With speed at the core of its design, there are still important issues in the FastTree-2 implementation that harm its performance and scalability. To deal with these limitations, we introduce VeryFastTree, a highly tuned implementation of the FastTree-2 tool that takes advantage of parallelization and vectorization strategies to boost performance. Results VeryFastTree is able to construct a tree on a standard server using double-precision arithmetic from an ultra-large 330k alignment in only 4.5 h, which is 7.8× and 3.5× faster than the sequential and best parallel FastTree-2 times, respectively. Availability and implementation VeryFastTree is available at the GitHub repository: https://github.com/citiususc/veryfasttree. Supplementary information Supplementary data are available at Bioinformatics online.

scholarly journals COMPUTING WATERTIGHT VOLUMETRIC MODELS FROM BOUNDARY REPRESENTATIONS TO ENSURE CONSISTENT TOPOLOGICAL OPERATIONS

2021 ◽  
Vol VIII-4/W2-2021 ◽  
pp. 21-28
Author(s):  
M. W. Jahn ◽  
P. E. Bradley
Keyword(s):  
Graph Model ◽  
3D Models ◽  
Double Precision ◽  
Data Set ◽  
Information Models ◽  
Volumetric Models ◽  
Double Precision Arithmetic ◽  
Boundary Representations ◽  
Definition Of ◽  
Spatial Entities

Abstract. To simulate environmental processes, noise, flooding in cities as well as the behaviour of buildings and infrastructure, ‘watertight’ volumetric models are a measuring prerequisite. They ensure topologically consistent 3D models and allow the definition of proper topological operations. However, in many existing city or other geo-information models, topologically unchecked boundary representations are used to store spatial entities. In order to obtain consistent topological models, including their ‘fillings’, in this paper, a triangulation combined with overlay and path-finding methods is presented by climbing up the dimension, beginning with the wireframe model. The algorithms developed for this task are presented, whereby using the philosophy of graph databases and the Property Graph Model. Examples to illustrate the algorithms are given, and experiments are performed on a data-set from Erfurt, Thuringia (Germany), providing complex geometries of buildings. The heavy influence of double precision arithmetic on the results, in particular the positional and angular precision, is discussed in the end.

scholarly journals Discrete Spherical Harmonic Transforms for Equiangular Grids of Spatial and Spectral Data

2011 ◽  
Vol 1 (1) ◽  
pp. 9-16 ◽  
Author(s):  
J. Blais
Keyword(s):  
Fourier Transform ◽  
Spectral Data ◽  
Spherical Harmonic ◽  
Fourier Transforms ◽  
Data Matrix ◽  
Geopotential Model ◽  
Double Precision ◽  
Analysis And Synthesis ◽  
Double Precision Arithmetic ◽  
Band Limited

Discrete Spherical Harmonic Transforms for Equiangular Grids of Spatial and Spectral DataSpherical Harmonic Transforms (SHTs) which are non-commutative Fourier transforms on the sphere are critical in global geopotential and related applications. Among the best known global strategies for discrete SHTs of band-limited spherical functions are Chebychev quadratures and least squares for equiangular grids. With proper numerical preconditioning, independent of latitude, reliable analysis and synthesis results for degrees and orders over 3800 in double precision arithmetic have been achieved and explicitly demonstrated using white noise simulations. The SHT synthesis and analysis can easily be modified for the ordinary Fourier transform of the data matrix and the mathematical situation is illustrated in a new functional diagram. Numerical analysis has shown very little differences in the numerical conditioning and computational efforts required when working with the two-dimensional (2D) Fourier transform of the data matrix. This can be interpreted as the spectral form of the discrete SHT which can be useful in multiresolution and other applications. Numerical results corresponding to the latest Earth Geopotential Model EGM 2008 of maximum degree and order 2190 are included with some discussion of the implications when working with such spectral sequences of fast decreasing magnitude.

Double Precision Is Not Needed for Many-Body Calculations: New Conventional Wisdom

2018 ◽  
Author(s):  
Pavel Pokhilko ◽  
Evgeny Epifanovsky ◽  
Anna I. Krylov
Keyword(s):  
Large Scale ◽  
Computation Time ◽  
Coupled Cluster ◽  
Double Precision ◽  
Many Body ◽  
Single Precision ◽  
Parallel Performance ◽  
Point Representation ◽  
Electron Repulsion Integrals ◽  
Cluster Methods

Using single precision floating point representation reduces the size of data and computation time by a factor of two relative to double precision conventionally used in electronic structure programs. For large-scale calculations, such as those encountered in many-body theories, reduced memory footprint alleviates memory and input/output bottlenecks. Reduced size of data can lead to additional gains due to improved parallel performance on CPUs and various accelerators. However, using single precision can potentially reduce the accuracy of computed observables. Here we report an implementation of coupled-cluster and equation-of-motion coupled-cluster methods with single and double excitations in single precision. We consider both standard implementation and one using Cholesky decomposition or resolution-of-the-identity of electron-repulsion integrals. Numerical tests illustrate that when single precision is used in correlated calculations, the loss of accuracy is insignificant and pure single-precision implementation can be used for computing energies, analytic gradients, excited states, and molecular properties. In addition to pure single-precision calculations, our implementation allows one to follow a single-precision calculation by clean-up iterations, fully recovering double-precision results while retaining significant savings.

Distribution and Correlation of the Coding Sequence Lengths in Bacterial Genomes

2008 ◽  
Vol 59 (11) ◽  
Author(s):  
Vasile V. Morariu
Keyword(s):  
Correlation Analysis ◽  
Exponential Function ◽  
Short Range ◽  
Statistical Physics ◽  
Bacterial Genomes ◽  
Coding Sequence ◽  
Correlation Properties ◽  
Short Range Correlations ◽  
Fluctuating System

The length of coding sequence (CDS) series in bacterial genomes were regarded as a fluctuating system and characterized by the methods of statistical physics. The distribution and the correlation properties of CDS for 47 genomes were investigated. The distribution was found to be approximated by an exponential function while the correlation analysis revealed short range correlations.

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