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• W595664544 abstract "This work aims at determining suitable scopes for several algorithms of interval matrices multiplication.First, we quantify the numerical quality. Former error analyses of interval matrix products establish bounds on the radius overestimation by neglecting the roundoff error. We discuss here several possible measures for interval approximations. We then bound the roundoff error and compare experimentally this bound with the global error distribution on several random data sets. This approach enlightens the relative importance of the roundoff and arithmetic errors depending on the value and homogeneity of relative accuracies of inputs, on the matrix dimension, and on the working precision. This also leads to a new algorithm that is cheaper yet as accurate as previous ones under well-identified conditions.Second, we exploit the parallelism of linear algebra. Previous implementations use calls to BLAS routines on numerical matrices. We show that this may lead to wrong interval results and also restrict the scalability of the performance when the core count increases. To overcome these problems, we implement a blocking version with OpenMP threads executing block kernels with vector instructions. The timings on a 4-octo-core machine show that this implementation is more scalable than the BLAS one and that the cost of numerical and interval matrix products are comparable." @default.
• W595664544 created "2016-06-24" @default.
• W595664544 creator A5036591565 @default.
• W595664544 date "2014-10-31" @default.
• W595664544 modified "2023-09-23" @default.
• W595664544 title "Numerical Quality and High Performance In Interval Linear Algebra on Multi-Core Processors" @default.
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• W595664544 hasPublicationYear "2014" @default.
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