arXiv subjects

Erin Claire Carson

Publications and source records attributed to Erin Claire Carson.

2 recordsLinked to original sources

arXiv2026

Balancing Inexactness in Mixed Precision Matrix Computations

Support for arithmetic in multiple precisions and number formats is becoming increasingly common in emerging high-performance architectures. From a computational scientist's perspective, our goal is to determine how and where we can safely exploit mixed precision computation in our codes to improve performance. One case where the use of low precision is natural, common in computational science, is when there are already other significant sources of ``inexactness'' present, e.g., discretization error, measurement error, or algorithmic approximation error. In such instances, analyzing the interaction of these different sources of inexactness can give insight into how the precisions of various computations should be chosen in order to ``balance'' the errors, potentially improving performance without a noticeable decrease in accuracy. We present a few recent examples of this approach which demonstrate the potential for the use of mixed precision in numerical linear algebra and matrix computations.

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arXiv2025

The Detection and Correction of Silent Errors in Pipelined Krylov Subspace Methods

As computational machines become larger and more complex, the probability of hardware failure rises. ``Silent errors'', or bit flips, may not be immediately apparent but can cause detrimental effects to algorithm behavior. In this work, we examine an algorithm-based approach to silent error detection in the context of pipelined Krylov subspace methods, in particular, Pipe-PR-CG, for the solution of linear systems. Our approach is based on using finite precision error analysis to bound the differences between quantities which should be equal in exact arithmetic. By monitoring select quantities during the iteration, we can detect when these bounds are violated, which indicates that a silent error has occurred. We use this approach to develop a fault-tolerant variant and also suggest a strategy for dynamically adapting the detection criteria. Our numerical experiments demonstrate the effectiveness of our approach.

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