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<p>This paper presents an Alternating Anderson–Variable Parameter Uzawa method for solving the indefinite least squares problem. The approach periodically incorporates Anderson acceleration into the underlying Variable Parameter Uzawa method, inheriting its unconditional convergence property while establishing <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(r\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>r</mi> </math></EquationSource> </InlineEquation>-linear convergence rates controlled by spectral radii. Algorithmic innovations include a structured acceleration framework reusing historical residuals and employing Gaussian Process Regression to optimize acceleration frequency and depth adaptively. Numerical experiments demonstrate significant computational advantages in both dense and sparse matrix systems compared to established benchmarks.</p>

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Alternating Anderson-Uzawa method for solving the indefinite least squares problem

  • 期刊论文

  • 发表日期：

    2025年9月11日

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  • Peizhe Li,
  • Kailiang Xin

摘要

This paper presents an Alternating Anderson–Variable Parameter Uzawa method for solving the indefinite least squares problem. The approach periodically incorporates Anderson acceleration into the underlying Variable Parameter Uzawa method, inheriting its unconditional convergence property while establishing \(r\) r -linear convergence rates controlled by spectral radii. Algorithmic innovations include a structured acceleration framework reusing historical residuals and employing Gaussian Process Regression to optimize acceleration frequency and depth adaptively. Numerical experiments demonstrate significant computational advantages in both dense and sparse matrix systems compared to established benchmarks.