A wavelet transform approach to inverse problems of Vandermonde type systems

Inverse problems of Vandermonde type systems have been solved using the discrete wavelet transform. The inverse matrices of the transformed subsystems were calculated, thereby locating the largest well-conditioned submatrix. The reduced system was solved and the solution was inversely transformed. Results were compared between two different wavelet basis functions, indicating that Daubechies-4 wavelets lead to much more accurate solutions than Haar wavelets. Three simple techniques for eliminating another systematic noise are also proposed to further improve the accuracy of the final solution.