A High-Order Fractional Parallel Scheme for Efficient Eigenvalue Computation
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...
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MDPI AG
2025-05-01
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| Series: | Fractal and Fractional |
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| author | Mudassir Shams Bruno Carpentieri |
| author_facet | Mudassir Shams Bruno Carpentieri |
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| description | 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>6</mn><mi>κ</mi><mo>+</mo><mn>4</mn></mrow></semantics></math></inline-formula>, where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>κ</mi><mo>∈</mo><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></mrow></semantics></math></inline-formula> 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. |
| format | Article |
| id | doaj-art-260d87b5b6264eeb9f2e31efbbdc63c0 |
| institution | Kabale University |
| issn | 2504-3110 |
| language | English |
| publishDate | 2025-05-01 |
| publisher | MDPI AG |
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| series | Fractal and Fractional |
| spelling | doaj-art-260d87b5b6264eeb9f2e31efbbdc63c02025-08-20T03:47:58ZengMDPI AGFractal and Fractional2504-31102025-05-019531310.3390/fractalfract9050313A High-Order Fractional Parallel Scheme for Efficient Eigenvalue ComputationMudassir Shams0Bruno Carpentieri1Faculty of Engineering, Free University of Bozen-Bolzano, 39100 Bolzano, ItalyFaculty of Engineering, Free University of Bozen-Bolzano, 39100 Bolzano, ItalyEigenvalue 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>6</mn><mi>κ</mi><mo>+</mo><mn>4</mn></mrow></semantics></math></inline-formula>, where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>κ</mi><mo>∈</mo><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></mrow></semantics></math></inline-formula> 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.https://www.mdpi.com/2504-3110/9/5/313fractional-order methodsparallel eigenvalue computationcomputational efficiencyfractal-based convergence analysishigh-performance numerical methods |
| spellingShingle | Mudassir Shams Bruno Carpentieri A High-Order Fractional Parallel Scheme for Efficient Eigenvalue Computation Fractal and Fractional fractional-order methods parallel eigenvalue computation computational efficiency fractal-based convergence analysis high-performance numerical methods |
| title | A High-Order Fractional Parallel Scheme for Efficient Eigenvalue Computation |
| title_full | A High-Order Fractional Parallel Scheme for Efficient Eigenvalue Computation |
| title_fullStr | A High-Order Fractional Parallel Scheme for Efficient Eigenvalue Computation |
| title_full_unstemmed | A High-Order Fractional Parallel Scheme for Efficient Eigenvalue Computation |
| title_short | A High-Order Fractional Parallel Scheme for Efficient Eigenvalue Computation |
| title_sort | high order fractional parallel scheme for efficient eigenvalue computation |
| topic | fractional-order methods parallel eigenvalue computation computational efficiency fractal-based convergence analysis high-performance numerical methods |
| url | https://www.mdpi.com/2504-3110/9/5/313 |
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