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<p>We propose the inertial parameterized Uzawa (iPU) method, a novel iterative solver for large sparse saddle point linear systems. By integrating inertial acceleration, a technique from optimization, into the classical parameterized Uzawa framework, the iPU method achieves faster convergence without losing computational simplicity. We establish convergence criteria for this two-step iterative scheme, deriving explicit parameter conditions that ensure spectral radius guarantees for the iteration matrix. Numerical experiments on the various test problems show that iPU outperforms some existing iterative methods (ASOR, MSSOR, ASSOR, GSOR), requiring fewer iterations and achieving the competitive computational time across different problem scales. These results demonstrate the effectiveness of inertial acceleration in enhancing Uzawa-type methods, positioning iPU as a reliable choice for high-dimensional saddle point problems.</p>

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An inertial-type parameterized Uzawa method for solving saddle point linear systems

  • 期刊论文

  • 发表日期：

    2026年3月30日

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  • Fahimeh Alipour,
  • Mohammad Reza Eslahchi,
  • Masoud Hajarian

摘要

We propose the inertial parameterized Uzawa (iPU) method, a novel iterative solver for large sparse saddle point linear systems. By integrating inertial acceleration, a technique from optimization, into the classical parameterized Uzawa framework, the iPU method achieves faster convergence without losing computational simplicity. We establish convergence criteria for this two-step iterative scheme, deriving explicit parameter conditions that ensure spectral radius guarantees for the iteration matrix. Numerical experiments on the various test problems show that iPU outperforms some existing iterative methods (ASOR, MSSOR, ASSOR, GSOR), requiring fewer iterations and achieving the competitive computational time across different problem scales. These results demonstrate the effectiveness of inertial acceleration in enhancing Uzawa-type methods, positioning iPU as a reliable choice for high-dimensional saddle point problems.