An algorithm for two-variable rational interpolation is developed. The algorithm is suitable for interpolation cases where neither the number of interpolation points nor the final degrees of the rational interpolant are known a priori. Instead, a maximum degree for the interpolant's numerator and denominator is assumed. By testing the condition number of the interpolation system's matrix at each step, the necessary reductions are made in order to cope with nonnormality and unattainability occasions. The algorithm can be used for applications of the Evaluation–Interpolation technique in matrix manipulations, such as finding the inverse of a matrix with elements rational functions of two variables. Symbolic calculations are completely avoided, thus keeping the execution time very low even if the system size is large. Most importantly, the algorithm achieves accurate function recoveries for greater polynomial degrees than other bivariate rational interpolation methods.

中文翻译：

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一种适用于矩阵操作的二变量有理插值算法

开发了一种二变量有理插值算法。该算法适用于插值点的数量和有理插值的最终度数都不是先验已知的插值情况。相反，假定插值的分子和分母的最大次数。通过在每一步测试插值系统矩阵的条件数，进行必要的缩减，以应对非正态性和无法达到的情况。该算法可用于评估-插值技术在矩阵操作中的应用，例如找到具有两个变量的元素有理函数的矩阵的逆矩阵。完全避免了符号计算，因此即使系统规模很大，也能保持非常低的执行时间。最重要的是，