In this paper, we perform a roundoff error analysis of an integration-based method for computing the matrix sign function recently proposed by Nakaya and Tanaka. The method expresses the matrix sign function using an integral representation and computes the integral numerically by the double-exponential formula. While the method has large-grain parallelism and works well for well-conditioned matrices, its accuracy deteriorates when the input matrix is ill-conditioned or highly nonnormal. We investigate the reason for this phenomenon by a detailed roundoff error analysis.

翻译：本文对Nakaya和Tanaka近期提出的基于积分的矩阵符号函数计算方法进行了舍入误差分析。该方法通过积分表示矩阵符号函数，并利用双指数公式对积分进行数值计算。尽管该方法具有粗粒度并行性，且对良态矩阵效果良好，但当输入矩阵呈病态或高度非正规时，其精度会显著下降。我们通过详细的舍入误差分析探究了这一现象的成因。