Preliminary Theoretical Analysis of Mixed Precision Krylov Subspace Methods (Q3 Report)
- Charles Univ., Prague (Czech Republic); Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
The third quarter of the project was spent performing theoretical finite precision analysis of Krylov subspace method variants that use mixed precision. Our focus here is on the Conjugate Gradient (CG) method and the Lanczos method. We have performed an analysis of maximum attainable accuracy for the classical CG method in which 3 precisions are used: a working precision ε, a precision εIP for the inner product computations, and a precision εMV for the matrix-vector products. Our results show that performing inner product computations in lower precision does not affect the attainable accuracy. Further, we have performed a complete error analysis of the s-step Lanczos algorithm. In this case, we show that the numerical behavior of the algorithm can be significantly improved by using extra precision in a small part of the computation. We summarize the main theorems in the remainder of the document. Other activities include attending biweekly xSDK meetings. The subsequent quarter will be spent finalizing these results into technical reports and/or manuscripts for submission to journals, as well as identifying opportunities for future work.
- Research Organization:
- Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States); Charles Univ., Prague (Czech Republic)
- Sponsoring Organization:
- USDOE National Nuclear Security Administration (NNSA)
- DOE Contract Number:
- AC52-07NA27344
- OSTI ID:
- 1755809
- Report Number(s):
- LLNL-SR--818012; 1028358
- Country of Publication:
- United States
- Language:
- English
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