A new algorithm for the evaluation of the incomplete gamma function on vector computers

@article{Frchtl1994ANA,
  title={A new algorithm for the evaluation of the incomplete gamma function on vector computers},
  author={H. Fr{\"u}chtl and P. Otto},
  journal={ACM Trans. Math. Softw.},
  year={1994},
  volume={20},
  pages={436-446}
}
Several methods of evaluating the Incomplete Gamma Function are compared according to accuracy and computation time. An improved algorithm is presented which allows significantly faster computation of two-electron integrals on most vector computers, especially in the case of GLO functions. Parameters for <italic>F<subscrpt>0</subscrpt>(t)</italic> are tabulated. 

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References

SHOWING 1-10 OF 10 REFERENCES
Methods for efficient evaluation of integrals for Gaussian type basis sets
Methods are described that allow for an efficient evaluation of two-electron integrals over contracted Gaussian lobe functions. The improvement in computational speed is achieved by avoiding theExpand
Approximations for the Functions Fm(z) Occurring in Molecular Calculations with a Gaussian Basis
Approximations, accurate to ± 1 × 10−8, have been developed for the functions Fm(z) which arise in molecular calculations using Gaussian basis functions. These are found to reduce integralExpand
Nonlinear Sequence Transformations for the Efficient Evaluation of Auxiliary Functions for GTO Molecular Integrals
It is discussed how the auxiliary function F m (z) with m ∈ ℕ0 and z ∈ ℝ+ can be computed efficiently by means of some recently discovered nonlinear sequence transformations. It is shown that the newExpand
Numerical integration using rys polynomials
Abstract We define and discuss the properties of manifolds of polynomials J n ( t , x ) and R n ( t , x ), called Rys polynomials, which are orthonormal with respect to the weighting factor exp(− xtExpand
Parallelization and Vectorization of Quantum Mechanical Methods - I. Integral Program for Polymers and Molecules
TLDR
New integral programs (one- and two-electron integrals) for multiprocessor systems with special emphasis on vectorizable structures and algorithms are developed and prove that for large chemical systems the parallelization will be very efficient. Expand
Bemerkungen zum Self-consistent-field-Verfahren und zur Methode der Konfigurationenwechselwirkung in der Quantenchemie
Für die Self-consistent-field-Methode wird eine Möglichkeit angegeben, die es erlaubt, ohne die Methode in ihrer mathematischen Form abzuändern, bessere Einelektronen-Molekülfunktionen zu erhalten,Expand
KGNMOL: A Program for Large Molecules and Molecular Interaction
Numerwal Determmatmn of the Electronic Structure of Atoms
  • 1989
Approximations for digital computers
Theoret Chzm. Acts
  • Theoret Chzm. Acts