NUMERICAL INTEGRATION OF ANALYTIC FUNCTIONS USING HYBRID CLENSHAW-CURTIS ADAPTIVE QUADRATURE ROUTINE

2020 ◽  
Vol 126 (2) ◽  
pp. 153-168
Author(s):  
Debasish Das ◽  
Pandit Jagatananda Mishra ◽  
Rajani Ballav Dash
Keyword(s):  
Numerical Integration ◽  
Analytic Functions ◽  
Adaptive Quadrature

Numerical integration of analytic functions

2012 ◽  
Author(s):  
Gradimir V. Milovanović ◽  
Dobrilo e Tošić ◽  
Miloljub Albijanić
Keyword(s):  
Numerical Integration ◽  
Analytic Functions

scholarly journals A quadrature rule of Lobatto-Gaussian for numerical integration of analytic functions

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Sanjit Kumar Mohanty ◽  
Rajani Ballav Dash
Keyword(s):  
Theoretical Prediction ◽  
Numerical Integration ◽  
Error Estimation ◽  
Analytic Functions ◽  
Quadrature Rule ◽  
Asymptotic Error

<p style='text-indent:20px;'>A novel quadrature rule is formed combining Lobatto six point transformed rule and Gauss-Legendre five point transformed rule each having precision nine. The mixed rule so formed is of precision eleven. Through asymptotic error estimation the novelty of the quadrature rule is justified. Some test integrals have been evaluated using the mixed rule and its constituents both in non-adaptive and adaptive modes. The results are found to be quite encouraging for the mixed rule which is in conformation with the theoretical prediction.</p>

scholarly journals Assessment of OpenMP Master–Slave Implementations for Selected Irregular Parallel Applications

Electronics ◽  
2021 ◽  
Vol 10 (10) ◽  
pp. 1188
Author(s):  
Paweł Czarnul
Keyword(s):  
Numerical Integration ◽  
Input Data ◽  
Region Of Interest ◽  
Point Of View ◽  
The Other ◽  
Parallel Applications ◽  
Data Generation ◽  
Adaptive Quadrature ◽  
Application Point ◽  
Computing Accuracy

The paper investigates various implementations of a master–slave paradigm using the popular OpenMP API and relative performance of the former using modern multi-core workstation CPUs. It is assumed that a master partitions available input into a batch of predefined number of data chunks which are then processed in parallel by a set of slaves and the procedure is repeated until all input data has been processed. The paper experimentally assesses performance of six implementations using OpenMP locks, the tasking construct, dynamically partitioned for loop, without and with overlapping merging results and data generation, using the gcc compiler. Two distinct parallel applications are tested, each using the six aforementioned implementations, on two systems representing desktop and worstation environments: one with Intel i7-7700 3.60GHz Kaby Lake CPU and eight logical processors and the other with two Intel Xeon E5-2620 v4 2.10GHz Broadwell CPUs and 32 logical processors. From the application point of view, irregular adaptive quadrature numerical integration, as well as finding a region of interest within an irregular image is tested. Various compute intensities are investigated through setting various computing accuracy per subrange and number of image passes, respectively. Results allow programmers to assess which solution and configuration settings such as the numbers of threads and thread affinities shall be preferred.

Numerical Integration of Non-analytic Functions

1964 ◽  
Vol 43 (1-4) ◽  
pp. 45-50 ◽  
Author(s):  
P C Waterman ◽  
J. M. Yos ◽  
R J. Abodeely
Keyword(s):  
Numerical Integration ◽  
Analytic Functions

scholarly journals A generalized Birkhoff–Young quadrature formula

2016 ◽  
Vol 32 (2) ◽  
pp. 203-213
Author(s):  
GRADIMIR V. MILOVANOVIC ◽  
◽  
MILOLJUB ALBIJANIC ◽  
Keyword(s):  
Numerical Integration ◽  
Explicit Form ◽  
Quadrature Formula ◽  
Analytic Functions ◽  
Maximal Degree ◽  
Special Cases

A generalized (4n + 1)-point Birkhoff–Young quadrature of interpolatory type with the maximal degree of precision for numerical integration of analytic functions is derived. An explicit form of the node polynomial of such kind of quadratures is obtained. Special cases and an example are presented.

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