论文标题
某些男性含有理性近似值的单位性
Unitarity of some barycentric rational approximants
论文作者
论文摘要
指数函数将假想轴映射到单位圆，对于许多应用，此单位性属性也是理想的近似值。我们表明，该特性不仅是由（k，k） - 理性的barycentric interpolant保守的，而且还通过（k，k） - 理性的barycentric近似因素，从而最大程度地减少线性化近似误差。这些结果是与线性近似误差相关的Loewner型矩阵的单数矢量的某些特性的结果。该类别的重要代表是由自适应的Antoulas-Anderson（AAA）方法和AAA-LAWSON方法计算的有理近似值。我们的结果还导致修改过程，并提高了单位性属性的数值稳定性并降低了计算成本。
The exponential function maps the imaginary axis to the unit circle and, for many applications, this unitarity property is also desirable from its approximations. We show that this property is conserved not only by the (k,k)-rational barycentric interpolant of the exponential on the imaginary axis, but also by (k,k)-rational barycentric approximants that minimize a linearized approximation error. These results are a consequence of certain properties of singular vectors of Loewner-type matrices associated to linearized approximation errors. Prominent representatives of this class are rational approximants computed by the adaptive Antoulas--Anderson (AAA) method and the AAA--Lawson method. Our results also lead to a modified procedure with improved numerical stability of the unitarity property and reduced computational cost.
