Efficient iterative solutions to complex-valued nonlinear least-squares problems with mixed linear and antilinear
Tae Hyung Kim1, Justin P Haldar1
1Department of Electrical and Computer Engineering, University of Southern California, Los Angeles, CA 90089, USA.
Optimization and Engineering
|June 3, 2022
Summary
This study presents a new method for solving complex nonlinear least-squares problems involving linear and antilinear operators. The approach simplifies implementation and reduces computational complexity for iterative solutions.
Area of Science:
- Applied Mathematics
- Computational Science
- Signal Processing
Background:
- Classical linear least-squares problems have established solutions.
- Nonlinear least-squares problems with mixed linear/antilinear operators are complex.
- Existing methods map these problems to real-valued domains, increasing complexity.
Purpose of the Study:
- To develop theory and computational methods for solving mixed linear/antilinear least-squares problems.
- To retain the complex-valued structure of the original inverse problem.
- To simplify implementation and reduce computational complexity of iterative algorithms.
Main Methods:
- Developing iterative solution algorithms for mixed linear/antilinear least-squares problems.
- Utilizing standard linear least-squares tools within a complex-valued framework.
- Retaining the original complex-valued structure throughout the solution process.
Main Results:
- Demonstrated a novel approach to solve complex nonlinear least-squares problems.
- Showcased simplification in implementation compared to real-valued mappings.
- Illustrated reduction in computational complexity for iterative solutions.
Conclusions:
- The proposed methods effectively solve mixed linear/antilinear least-squares problems.
- This approach offers practical advantages in implementation and computational efficiency.
- The technique preserves the inherent complex structure of the inverse problem.
Keywords:
15A2947J0547J2547N1065H1065K10Efficient numerical computationsInverse problemsIterative least-squares algorithmsLinear and antilinear operatorsMore Related Videos
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