The detection and correction of silent errors in pipelined Krylov subspace methods

Area of Science:

• Computer Science
• Numerical Analysis
• High-Performance Computing

Background:

• Increasing computational complexity raises hardware failure risks.
• Silent errors (bit flips) can subtly corrupt algorithm results.
• Pipelined Krylov subspace methods are crucial for solving large linear systems.

Purpose of the Study:

• To develop an algorithm-based silent error detection method for pipelined Krylov subspace methods.
• To enhance the reliability of numerical computations in complex systems.
• To address the challenge of undetected hardware faults in scientific computing.

Main Methods:

• Utilizing finite precision error analysis to establish bounds on computational quantities.
• Monitoring key variables during the iterative process to detect bound violations.
• Developing a fault-tolerant variant of the Pipe-PR-CG algorithm.
• Proposing dynamic adaptation strategies for error detection criteria.

Main Results:

• Demonstrated the effectiveness of the proposed silent error detection approach.
• Successfully developed a fault-tolerant version of the Pipe-PR-CG method.
• Numerical experiments validated the capability to identify silent errors.
• Showcased the potential for dynamic adjustment of detection sensitivity.

Conclusions:

• The algorithm-based approach provides a robust mechanism for detecting silent errors in pipelined Krylov methods.
• This method enhances the trustworthiness of numerical solutions derived from complex computational systems.
• The developed fault-tolerant variant and adaptive strategy offer practical improvements for reliable scientific computing.