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The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry

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Eigenvector determination by iterative optical methods.

B V Kumar, D Casasent

|April 8, 2010

Summary

This summary is machine-generated.

This study analyzes three power methods for computing matrix eigenvalues and eigenvectors on an iterative optical processor (IOP). The second method is identified as the most efficient for IOP implementation and processing speed.

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Area of Science:

Numerical analysis
Optical computing
Linear algebra

Background:

Eigenvalue and eigenvector computation is crucial for various scientific and engineering applications.
Iterative optical processors (IOPs) offer potential for high-speed matrix computations.

Purpose of the Study:

To analyze and compare three power methods for eigenvalue and eigenvector computation on an IOP.
To determine the most suitable method considering implementation and processing speed.

Main Methods:

Analysis of three distinct power iteration methods.
Evaluation of computational complexity and suitability for optical implementation.
Performance comparison based on processing speed and hardware constraints.

Main Results:

All three methods are viable for eigenvalue and eigenvector computation on an IOP.
The second analyzed power method demonstrates superior performance.
This method is preferable to recently described alternatives for IOPs.

Conclusions:

The second power method is recommended for eigenvalue and eigenvector calculations on iterative optical processors.
This method offers a balance of computational efficiency and practical implementation advantages.