IEEE Transactions on Computers · 1990 · 154 citations · 22 references
EngineeringComputer EngineeringComputer ScienceFault ToleranceFault-tolerant ComputingFault-tolerant SystemsCoding TheoryError DetectionError-correcting CodesHardware Fault ToleranceMatrix ComputationNumerical Linear AlgebraCodes Over Finite FieldsEncoding AlgorithmsFault Tolerant AlgorithmsFinite Field ArithmeticLinear CodesLu DecompositionPerformance OverheadPerformance Overhead Analysis
A generalization of existing real numer codes is proposed. It is proven that linearity is a necessary and sufficient condition for codes used for fault-tolerant matrix operations such as matrix addition, multiplication, transposition, and LU decomposition. It is also proven that for every linear code defined over a finite field, there exists a corresponding linear real-number code with similar error detecting capabilities. Encoding schemes are given for some of the example codes which fall under the general set of real-number codes. With the help of experiments, a rule is derived for the selection of a particular code for a given application. The performance overhead of fault tolerance schemes using the generalized encoding schemes is shown to be very low, and this is substantiated through simulation experiments.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>
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The Algebraic Eigenvalue Problem
E. I., J. H. Wilkinson · Mathematics of Computation · 1966 · 5.2K citations
R. G. Gallager, W. W. Peterson · Mathematics of Computation · 1962 · 2.1K citations
The algebraic eigenvalue problem
V.V. Voyevodin · USSR Computational Mathematics and Mathematical Physics · 1966 · 2.1K citations