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In this paper, we perform a roundoff error analysis of an integration-basedmethod for computing the matrix sign function recently proposed by Nakaya andTanaka. The method expresses the matrix sign function using an integralrepresentation and computes the integral numerically by the double-exponentialformula. While the method has large-grain parallelism and works well forwell-conditioned matrices, its accuracy deteriorates when the input matrix isill-conditioned or highly nonnormal. We investigate the reason for thisphenomenon by a detailed roundoff error analysis.

Roundoff error analysis of the double exponential formula-based method for the matrix sign function