New finite difference formulas for numerical differentiation

Authors: Istiaq Rasool Khan, Ryoji Ohba

Source: Journal of Computational and Applied Mathematics. 126:269-276

Subject Terms: finite difference formulas, Numerical differentiation, Computational Mathematics, Software, source code, etc. for problems pertaining to real functions, computer program, Applied Mathematics, Finite difference formulas, Taylor series, Nyquist frequency, Closed-form expressions, numerical differentiation, 0101 mathematics, 01 natural sciences

File Description: application/xml

Access URL: https://zbmath.org/1582366
https://doi.org/10.1016/s0377-0427(99)00358-1
https://ui.adsabs.harvard.edu/abs/2000JCoAM.126..269K/abstract
https://www.sciencedirect.com/science/article/pii/S0377042799003581

Closed-form expressions for the finite difference approximations of first and higher derivatives based on Taylor series

Authors: Ryoji Ohba, Ishtiaq Rasool Khan

Source: Journal of Computational and Applied Mathematics. 107:179-193

Subject Terms: Software, source code, etc. for problems pertaining to real functions, Applied Mathematics, Finite difference formula, ideal digital differentiator, Digital filter, 01 natural sciences, Numerical differentiation, Computational Mathematics, computer program, finite difference approximations, Taylor series, closed-form expressions, numerical differentiation, 0101 mathematics

File Description: application/xml

Access URL: https://zbmath.org/1331024
https://doi.org/10.1016/s0377-0427(99)00088-6
https://www.sciencedirect.com/science/article/pii/S0377042799000886
https://www.sciencedirect.com/science/article/abs/pii/S0377042799000886

Algorithm 755: ADOL-C: a package for the automatic differentiation of algorithms written in C/C++

Authors: Jean Utke, David W. Juedes, Andreas Griewank

Source: ACM Transactions on Mathematical Software. 22:131-167

Subject Terms: gradients, Taylor coefficients, Software, source code, etc. for problems pertaining to real functions, 0211 other engineering and technologies, C++ package ADOL-C, 02 engineering and technology, automatic differentiation, 01 natural sciences, reverse mode, overloading, Numerical differentiation, Packaged methods for numerical algorithms, chain rule, 0101 mathematics, forward mode, Hessians, derivatives of vector functions

File Description: application/xml

Access URL: https://dl.acm.org/citation.cfm?id=229474
https://doi.org/10.1145/229473.229474
https://dblp.uni-trier.de/db/journals/toms/toms22.html#GriewankJU96
https://doi.acm.org/10.1145/229473.229474
https://dl.acm.org/doi/abs/10.1145/229473.229474

Highly accurate tables for elementary functions

Authors: Wolfram Luther

Source: BIT Numerical Mathematics. 35:352-360

Subject Terms: computer arithmetic, tables of elementary functions, Computation of special functions and constants, construction of tables, Bresenham's algorithm, Software, source code, etc. for problems pertaining to real functions, 0202 electrical engineering, electronic engineering, information engineering, Elementary functions, 02 engineering and technology, 0101 mathematics, 01 natural sciences, Tables in numerical analysis

File Description: application/xml

Access URL: https://zbmath.org/827431
https://doi.org/10.1007/bf01732609
https://link.springer.com/content/pdf/10.1007/BF01732609.pdf
https://link.springer.com/article/10.1007/BF01732609

Ultra-high precision computations

Authors: E.L. Ortiz, H.G. Khajah

Source: Computers & Mathematics with Applications. 27:41-57

Subject Terms: tables, Software, source code, etc. for problems pertaining to real functions, ultra-high precision computations, tau method, Elementary functions, error bounds, 01 natural sciences, Computational Mathematics, Computation of special functions and constants, construction of tables, Fortran subroutine, Chebyshev expansions, Computational Theory and Mathematics, Modelling and Simulation, basic mathematical functions, 0101 mathematics, Tables in numerical analysis

File Description: application/xml

Access URL: https://www.sciencedirect.com/science/article/pii/0898122194901481
https://core.ac.uk/display/82204083
http://www.sciencedirect.com/science/article/pii/0898122194901481

Computer programs and mathematical proofs

Authors: Robert Gray

Source: The Mathematical Intelligencer. 13:45-48

Subject Terms: Methodology of mathematics, Theory of software, program design, Software, source code, etc. for problems pertaining to real functions, Heine-Borel theorem, proof design

File Description: application/xml

Access URL: https://zbmath.org/28914
https://doi.org/10.1007/bf03028342
https://link.springer.com/article/10.1007/BF03028342

Adaptive Quadrature—Revisited: Adaptive quadrature -- Revisited

Authors: Gander, Walter, Gautschi, Walter

Source: BIT Numerical Mathematics. 40:84-101

Subject Terms: QUADRATURE FORMULAS (NUMERICAL MATHEMATICS), NUMERISCHE FEHLER + FEHLERSCHÄTZUNG (NUMERISCHE MATHEMATIK), Software, source code, etc. for problems pertaining to real functions, Matlab programs, 02 engineering and technology, Numerical quadrature and cubature formulas, 01 natural sciences, Data processing, computer science, FOS: Mathematics, 0202 electrical engineering, electronic engineering, information engineering, Gauss-Kronrod formulas, NUMERICAL INTEGRATION (NUMERICAL MATHEMATICS), 0101 mathematics, MATLAB (SOFTWARE FOR NUMERICAL COMPUTATION), QUADRATURFORMELN (NUMERISCHE MATHEMATIK), Gauss-Lobatto formula, NUMERICAL ERRORS + ERROR ESTIMATION (NUMERICAL MATHEMATICS), MATLAB (SOFTWARE FÜR NUMERISCHE BERECHNUNG), NUMERISCHE INTEGRATION (NUMERISCHE MATHEMATIK), Approximate quadratures, Simpson rule, adaptive quadrature, Mathematics

File Description: application/xml; application/application/pdf

Access URL: https://zbmath.org/1471140
https://doi.org/10.1023/a:1022318402393
https://www.research-collection.ethz.ch/handle/20.500.11850/69327
https://link.springer.com/article/10.1023/A%3A1022318402393
http://hdl.handle.net/20.500.11850/69327

Vector 33: A reduce program for vector algebra and calculus in orthogonal curvilinear coordinates: VECTOR 33: A REDUCE program for vector algebra and calculus in orthogonal curvilinear coordiantes

Authors: David J. Harper

Source: Computer Physics Communications. 54:295-305

Subject Terms: REDUCE 3.3, Software, source code, etc. for problems pertaining to real functions, Other matrix algorithms, algebra and calculus operations, Symbolic computation and algebraic computation, 01 natural sciences, gradient, Numerical differentiation, orthogonal curvilinear coordinates, curl, dot product, 0103 physical sciences, Calculus of vector functions, cross product, program, numerical differentiation, Laplacian, divergence

File Description: application/xml

Access URL: https://zbmath.org/609696
https://doi.org/10.1016/0010-4655(89)90092-1
https://www.sciencedirect.com/science/article/pii/0010465589900921
http://ui.adsabs.harvard.edu/abs/1989CoPhC..54..295H/abstract

Numerical differentiation of tabulated functions with automatic choice of step‐size: Numerical differentiation of tabulated functions with automatic choice of step-size

Authors: John Michael McNamee

Source: International Journal for Numerical Methods in Engineering. 21:1171-1185

Subject Terms: Numerical differentiation, stepsize, Software, source code, etc. for problems pertaining to real functions, Fortran program, total error, smoothing, truncation error, 0101 mathematics, tabulated function, comparison of methods, 01 natural sciences

File Description: application/xml

Access URL: https://zbmath.org/3932283
https://doi.org/10.1002/nme.1620210702
https://onlinelibrary.wiley.com/doi/abs/10.1002/nme.1620210702
https://ui.adsabs.harvard.edu/abs/1985IJNME..21.1171M/abstract

A pipelined computer architecture for unified elementary function evaluation

Authors: Daniel A. Eggerding, Michael Andrews

Source: Computers & Electrical Engineering. 5:189-202

Subject Terms: Cellular automata (computational aspects), Iterative Arrays, Pipelined Computer Architecture, Hyperbolic Function, Software, source code, etc. for problems pertaining to real functions, Elementary Function, 02 engineering and technology, Computer aspects of numerical algorithms, Trigonometric Function, Theory of operating systems, Past Fourier Transform, 0202 electrical engineering, electronic engineering, information engineering, Algorithms in computer science, Software, source code, etc. for problems pertaining to special functions, Algorithms

File Description: application/xml

Access URL: https://zbmath.org/3609123
https://doi.org/10.1016/0045-7906(78)90030-7
https://www.sciencedirect.com/science/article/pii/0045790678900307

On Bairstow’s method for the solution of polynomial equations: On Bairstow's method for the solution of polynomial equations

Authors: Kenneth W. Brodlie

Source: Mathematics of Computation. 29:816-826

Subject Terms: Software, source code, etc. for problems pertaining to real functions, 4. Education, Software, source code, etc. for problems pertaining to functions of a complex variable, Polynomials in real and complex fields: factorization, Polynomials in real and complex fields: location of zeros (algebraic theorems), 02 engineering and technology, 01 natural sciences, Real polynomials: location of zeros, Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral), 0103 physical sciences, 0202 electrical engineering, electronic engineering, information engineering, Numerical computation of solutions to single equations, 0101 mathematics, Algorithms in computer science

File Description: application/xml

Access URL: https://www.ams.org/mcom/1975-29-131/S0025-5718-1975-0381283-7/S0025-5718-1975-0381283-7.pdf
https://zbmath.org/3511509
https://doi.org/10.2307/2005292
https://www.jstor.org/stable/2005292
https://www.ams.org/mcom/1975-29-131/S0025-5718-1975-0381283-7/S0025-5718-1975-0381283-7.pdf
https://www.ams.org/journals/mcom/1975-29-131/S0025-5718-1975-0381283-7/home.html

Numerical integration over a spherical shell: Numericl integration over a spherical shell

Authors: M. Sarrazin, M. Defranceschi

Source: Computer Physics Communications. 52:409-414

Subject Terms: Software, source code, etc. for problems pertaining to real functions, three dimensional integrals, 0103 physical sciences, Multidimensional problems, spherical coordinate grid, program, Numerical quadrature and cubature formulas, 01 natural sciences, Approximate quadratures

File Description: application/xml

Access URL: https://zbmath.org/609705
https://doi.org/10.1016/0010-4655(89)90115-x
http://ui.adsabs.harvard.edu/abs/1989CoPhC..52..409D/abstract
https://www.sciencedirect.com/science/article/abs/pii/001046558990115X

A Monte Carlo method for high dimensional integration

Authors: Ogata, Yosihiko

Source: Numerische Mathematik. 55:137-157

Subject Terms: 0301 basic medicine, high dimensional integration, Software, source code, etc. for problems pertaining to real functions, 4. Education, Multidimensional problems, Monte Carlo methods, crude Monte Carlo method, Metropolis Monte Carlo algorithm, Numerical quadrature and cubature formulas, 01 natural sciences, Article, Approximate quadratures, high dimensional functions, numerical example, 03 medical and health sciences, 510.mathematics, numerical integration, FORTRAN program, 0101 mathematics, numerical experiments

File Description: application/xml; image/jpeg; application/pdf

Access URL: https://zbmath.org/4096666
https://doi.org/10.1007/bf01406511
https://link.springer.com/article/10.1007%2FBF01406511
https://eudml.org/doc/133348
https://rd.springer.com/article/10.1007/BF01406511

Derivation and implementation of an algorithm for singular integrals

Authors: CALIO', FRANCA, MARCHETTI, ELENA MARIA

Source: Computing. 38:235-245

Subject Terms: numerical examples, weight function, Software, source code, etc. for problems pertaining to real functions, algebraic and logarithmic singularities, FORTRAN program, Gaussian quadrature rules, comparisons, Numerical quadrature and cubature formulas, Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane, Approximate quadratures

File Description: application/xml

Access URL: https://link.springer.com/article/10.1007/BF02240098
https://link.springer.com/content/pdf/10.1007/BF02240098.pdf
https://dblp.uni-trier.de/db/journals/computing/computing38.html#CalioM87
https://hdl.handle.net/11311/565577

Axiomatisation des manipulations symboliques en calcul des prédicats

Authors: Henry Kanoui, Marc Bergman

Source: Mémoires de la Société mathématique de France. 1:15-30

Subject Terms: Theory of software, Software, source code, etc. for problems pertaining to real functions, Combinatory logic and lambda calculus, Classical first-order logic, Symbolic computation and algebraic computation, Software, source code, etc. for problems pertaining to mathematical logic and foundations

File Description: application/xml

Access URL: http://www.numdam.org/article/MSMF_1977__49-50__15_0.pdf
https://zbmath.org/3597875
http://www.numdam.org/item?id=MSMF_1977__49-50__15_0

Automation of the manipulation of multivariate power series

Authors: G W Forbes

Source: Journal of Computational and Applied Mathematics. 15:37-58

Subject Terms: Multivariate power series, reversion, Software, source code, etc. for problems pertaining to real functions, Applied Mathematics, weighted truncation, algorithms, Series expansions (e.g., Taylor, Lidstone series, but not Fourier series), Symbolic computation and algebraic computation, 01 natural sciences, multivariate power series, Real-analytic functions, algebraic operations, Computational Mathematics, composition, Numerical summation of series, 0103 physical sciences, Calculus of vector functions, 0101 mathematics, power series manipulation

File Description: application/xml

Access URL: https://zbmath.org/4020292
https://doi.org/10.1016/0377-0427(86)90237-2
https://researchers.mq.edu.au/en/publications/automation-of-the-manipulation-of-multivariate-power-series
https://www.sciencedirect.com/science/article/abs/pii/0377042786902372
https://core.ac.uk/display/82363642
https://www.sciencedirect.com/science/article/pii/0377042786902372

Abscissae and weights for the Gauss-Laguerre quadrature formula

Authors: Tadashi Takemasa

Source: Computer Physics Communications. 52:133-140

Subject Terms: Newton-Raphson method, Software, source code, etc. for problems pertaining to real functions, 0103 physical sciences, Laguerre polynomials, program, weights, Gauss-Laguerre quadrature formula, Numerical quadrature and cubature formulas, abscissae, 01 natural sciences, Approximate quadratures

File Description: application/xml

Access URL: https://www.sciencedirect.com/science/article/pii/0010465588901786
https://ui.adsabs.harvard.edu/abs/1988CoPhC..52..133T/abstract
http://www.sciencedirect.com/science/article/pii/0010465588901786

A Simple Theorem on Riemann Integration, Based on Classroom Experience: A simple theorem on Riemann integration, based on classroom experience

Authors: Lance D. Drager

Source: SIAM Review. 25:255-259

Subject Terms: Software, source code, etc. for problems pertaining to real functions, computer program, Numerical integration, 0103 physical sciences, Riemann integration, 0101 mathematics, Integrals of Riemann, Stieltjes and Lebesgue type, 01 natural sciences, classroom demonstration

File Description: application/xml

Access URL: https://www.jstor.org/stable/2030217
https://epubs.siam.org/doi/abs/10.1137/1025048
https://dlnext.acm.org/doi/10.1137/1025048

Properly rounded variable precision square root

Authors: A. Abrham, T. E. Hull

Source: ACM Transactions on Mathematical Software. 11:229-237

Subject Terms: Computation of special functions and constants, construction of tables, square root, Software, source code, etc. for problems pertaining to real functions, certification and testing, 0202 electrical engineering, electronic engineering, information engineering, program, 02 engineering and technology, 0101 mathematics, variable precision, algorithm analysis, 01 natural sciences, Computer aspects of numerical algorithms, error analysis

File Description: application/xml

Access URL: https://dl.acm.org/doi/10.1145/214408.214413
http://dblp.uni-trier.de/db/journals/toms/toms11.html#HullA85
https://doi.acm.org/10.1145/214408.214413
https://dblp.uni-trier.de/db/journals/toms/toms11.html#HullA85

The average number of registers needed to evaluate a binary tree optimally

Authors: Rainer Kemp

Source: Acta Informatica. 11:363-372

Subject Terms: Enumeration, Graph theory (including graph drawing) in computer science, Software, source code, etc. for problems pertaining to real functions, Binary Tree, 0202 electrical engineering, electronic engineering, information engineering, Registers, 0102 computer and information sciences, 02 engineering and technology, Asymptotic Expansion, Algorithms in computer science, Software, source code, etc. for problems pertaining to special functions, 01 natural sciences

File Description: application/xml

Access URL: https://zbmath.org/3614191
https://doi.org/10.1007/bf00289094
https://dblp.uni-trier.de/db/journals/acta/acta11.html#Kemp79
https://link.springer.com/article/10.1007/BF00289094
https://link.springer.com/content/pdf/10.1007%2FBF00289094.pdf