A High-Order Fractional Parallel Scheme for Efficient Eigenvalue Computation

Abstract

Eigenvalue problems play a fundamental role in many scientific and engineering disciplines, including structural mechanics, quantum physics, and control theory. In this paper, we propose a fast and stable fractional-order parallel algorithm for solving eigenvalue problems. The method is implemented within a parallel computing framework, allowing simultaneous computations across multiple processors to improve both efficiency and reliability. A theoretical convergence analysis shows that the scheme achieves a local convergence order of 6 kappa+4, where kappa is an element of(0,1] denotes the Caputo fractional order prescribing the memory depth of the derivative term. Comparative evaluations based on memory utilization, residual error, CPU time, and iteration count demonstrate that the proposed parallel scheme outperforms existing methods in our test cases, exhibiting faster convergence and greater efficiency. These results highlight the method's robustness and scalability for large-scale eigenvalue computations.