# 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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NUMERICAL EVALUATION OF SPECIAL FUNCTIONS

- Computer Science
- 2001

The purpose of this paper is to assist in locating useful approximations and software for the numerical generation of higher transcendental functions, and to offer some suggestions for future developments in this field. Expand

#### References

SHOWING 1-10 OF 10 REFERENCES

Methods for efficient evaluation of integrals for Gaussian type basis sets

- Mathematics
- 1974

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 the… Expand

Approximations for the Functions Fm(z) Occurring in Molecular Calculations with a Gaussian Basis

- Physics
- 1971

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 integral… Expand

Nonlinear Sequence Transformations for the Efficient Evaluation of Auxiliary Functions for GTO Molecular Integrals

- Physics
- 1989

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 new… Expand

Numerical integration using rys polynomials

- Mathematics
- 1976

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(− xt… Expand

Parallelization and Vectorization of Quantum Mechanical Methods - I. Integral Program for Polymers and Molecules

- Computer Science
- Comput. Chem.
- 1993

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

- Chemistry
- 1956

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

Numerwal Determmatmn of the Electronic Structure of Atoms

- 1989

Theoret Chzm. Acts

- Theoret Chzm. Acts