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A fast algorithm for computing the Boys function.

Gregory Beylkin¹, Sandeep Sharma²

¹Department of Applied Mathematics, University of Colorado, Boulder, Colorado 80309, USA.

The Journal of Chemical Physics

|November 7, 2021

Summary

This summary is machine-generated.

A new fast algorithm computes the Boys function using nonlinear exponential approximation. This method efficiently evaluates the Boys function for real and complex arguments, matching existing algorithms.

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Area of Science:

Computational physics
Numerical analysis

Background:

The Boys function is crucial in various physics and chemistry calculations.
Existing algorithms for computing the Boys function can be computationally intensive.

Purpose of the Study:

To develop a novel, fast algorithm for computing the Boys function.
To provide an efficient method for evaluating the Boys function with both real and complex arguments.

Main Methods:

The study introduces a new algorithm based on a nonlinear approximation of the Boys function's integrand.
The approximation utilizes exponential functions for enhanced computational speed.
The algorithm is designed to handle both real and complex-valued arguments.

Main Results:

The developed algorithm demonstrates significant speed improvements for Boys function computation.
The algorithm achieves accuracy competitive with established methods.
It successfully evaluates the Boys function across real and complex domains.

Conclusions:

The new algorithm offers an efficient and accurate alternative for Boys function computation.
This advancement has implications for accelerating calculations in fields relying on the Boys function.