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The use of control theory to study iterative algorithms, which can be considered as dynamical systems, opens many opportunities to find new tools for analysis of algorithms. In this paper we show that results from the study of quantization effects in control systems can be used to find systematic ways for forward error analysis of iterative algorithms. The(More)
—It has been known for at least five decades that control theory can be used to study iterative algorithms. However, little work can be found in the control systems literature on numerical algorithms, especially on the study of finite precision effects. In this paper, we consider numerical iterative algorithms in finite precision as dynamical systems and(More)
— We present a new direct algorithm for solving a system of linear equations with a positive definite matrix by discretizing a continuous-time dynamical system for a large sampling time. The obtained algorithm is highly fine-grain parallelizable and its computational complexity grows logarithmically with respect to the condition number of the system of(More)
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