Optimizing diffraction catastrophe evaluation

Area of Science:

• Theoretical physics
• Computational optics

Background:

• Power series expansions are used for evaluating diffraction catastrophes.
• Recent numerical experiments showed accelerated convergence.

Purpose of the Study:

• To theoretically analyze power series expansions for diffraction catastrophes.
• To interpret numerical experiment results.
• To provide optimization criteria for diffraction catastrophe evaluations.

Main Methods:

• Theoretical analysis of power series expansions.
• Investigation of convergence properties.
• Application of the Weniger transformation.

Main Results:

• Hyperlinear convergence is identified as a key characteristic of these expansions.
• The Weniger transformation significantly accelerates numerical evaluations.
• Analytical expressions for optimizing diffraction catastrophe evaluations are derived.

Conclusions:

• The theoretical analysis provides a framework for understanding accelerated convergence in diffraction catastrophe computations.
• Numerical optimization of diffraction catastrophe evaluations can be achieved using the derived criteria.