Accuracy Improvement of Cubic Polynomial Inter/Extrapolation of MoM Matrices by Optimizing Frequency Samples

A cubic polynomial inter/extrapolation method is investigated to improve the inter/extrapolation accuracy of the matrix over a frequency band in the method of moments (MoM). In the method, the error of the MoM matrix in the Frobenius norm can be expressed as a product of the error coefficient and the polynomial component. The error coefficient is insensitive to the positions of the frequency samples and the operating frequency, and hence it is practical to minimize the amplitude of the polynomial component rather than the error of matrix by optimizing the frequency samples. Actually, the amplitude of the polynomial component attains the minimum when the frequency samples are analytically expressed in terms of the roots of the Chebyshev polynomial of degree 4. Numerical examples are presented to validate the proposed method.