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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
PubMed
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.

Keywords:
15A2947J0547J2547N1065H1065K10Efficient numerical computationsInverse problemsIterative least-squares algorithmsLinear and antilinear operators

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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.