Numerically stable real number codes based on random matrices

Authors:
Zizhong Chen;Jack Dongarra
Affiliations:
Computer Science Department, University of Tennessee, Knoxville, Knoxville, TN;Computer Science Department, University of Tennessee, Knoxville, Knoxville, TN
Venue:
ICCS'05 Proceedings of the 5th international conference on Computational Science - Volume Part I
Year:
2005

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Abstract

Error correction codes defined over real-number field have been studied and recognized as useful in many applications. However, most real-number codes in literature are quite suspect in their numerical stability. In this paper, we introduce a class of real-number codes based on random generator matrices over real-number fields. Codes over complex-number field are also discussed. Experiment results demonstrate our codes are numerically much more stable than existing codes in literature.