Fast Hankel transform of nth order with improved performance

Area of Science:

• Numerical Analysis
• Applied Mathematics
• Signal Processing

Background:

• The Hankel transform is crucial in various scientific fields, including physics and engineering.
• Accurate and efficient numerical computation of the Hankel transform is essential for solving complex problems.
• Existing algorithms may face limitations in speed or accuracy for higher-order transforms.

Purpose of the Study:

• To present a novel, improved algorithm for the numerical computation of the nth-order Hankel transform.
• To enhance the efficiency and accuracy of Hankel transform calculations.
• To validate the algorithm's performance using established functions.

Main Methods:

• Development of an improved numerical algorithm specifically designed for the nth-order Hankel transform.
• Rigorous testing and validation of the algorithm using a selection of well-known mathematical functions.
• Comparative analysis with existing numerical methods (if applicable, though not explicitly stated in the abstract).

Main Results:

• The presented algorithm provides accurate numerical computations for the nth-order Hankel transform.
• Successful application and validation of the algorithm across various well-known functions.
• Demonstration of improved performance (accuracy/efficiency) compared to baseline methods (implied by 'improved').

Conclusions:

• The developed algorithm offers a reliable and effective tool for the numerical computation of nth-order Hankel transforms.
• The findings support the utility of this improved algorithm in scientific and engineering applications requiring Hankel transform analysis.
• Further research could explore its application to more complex or specialized functions.