一种改进三角形矩阵函数计算的技巧
A Technique for Improving the Computation of Functions of Triangular Matrices
摘要：
我们提出了一个简单的技术，如果结合算法计算功能的三角形矩阵，可以使他们更有效。基本上，这种技术在于特定的缩放相似变换，其减少了三角形矩阵与正规性的偏离，从而降低了其范数，并且通常降低了其函数条件数。它可以很容易地扩展到非三角形矩阵，只要它是与算法相结合，涉及事先舒尔分解。将详细讨论应该使用或不使用该技术的情况。特别注意的是专门为特定的算法，如逆缩放和平方的矩阵对数和缩放和平方的矩阵指数。我们的建议的优点是支持的理论结果和数值实验说明。
英文摘要：
We propose a simple technique that, if combined with algorithms for computing functions of triangular matrices, can make them more efficient. Basically, such a technique consists in a specific scaling similarity transformation that reduces the departure from normality of a triangular matrix, thus decreasing its norm and in general its function condition number. It can easily be extended to non-triangular matrices, provided that it is combined with algorithms involving a prior Schur decomposition. Situations where the technique should be used or not will be discussed in detail. Special attention is devoted to particular algorithms like the inverse scaling and squaring to the matrix logarithm and the scaling and squaring to the matrix exponential. The advantages of our proposal are supported by theoretical results and illustrated with numerical experiments.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
