Preconditioned Random Toeplitz Operators
W. F. Ke, K. F. Lai, N. C. Wong
TL;DR
This paper investigates the effectiveness of preconditioned conjugate gradient methods for solving random Toeplitz systems, extending classical operator theory to the stochastic setting.
Contribution
It introduces a theoretical framework for applying preconditioned iterative methods to random Toeplitz operators, building on classical deterministic operator results.
Findings
Extended Brown-Halmos theory to random Toeplitz operators
Established convergence foundations for preconditioned conjugate gradient methods
Provided insights into spectral properties of random Toeplitz systems
Abstract
The solution of Hermitian positive definite random Toeplitz systems by the preconditioned conjugate gradient method for the Strang circulant preconditioner is studied. We established the foundation for this method by extending the work of Brown-Halmos on Toeplitz operators and Grenander-Szeg\"o on Teoplitz form to random Teoplitz operators.
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Taxonomy
TopicsRandom Matrices and Applications · Advanced Algebra and Geometry · Algebraic structures and combinatorial models