Chein-Shan Liu1
CMC-Computers, Materials & Continua, Vol.25, No.3, pp. 239-264, 2011, DOI:10.3970/cmc.2011.025.239
Abstract For the computational applications in several areas, we propose a single-scale and a multi-scale diagonal preconditioners to reduce the condition number of Vandermonde matrix. Then a new algorithm is given to solve the inversion of the resulting coefficient matrix after multiplying by a preconditioner to the Vandermonde matrix. We apply the new techniques to the interpolation of data by using very high-order polynomials, where the Runge phenomenon disappears even the equidistant nodes are used. In addition, we derive a new technique by employing an m-order polynomial with a multi-scale technique to interpolate 2m+1 data. Numerical results confirm the validity of… More >
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