TY  - EJOU
AU  - Liu, Chein-Shan 

TI  - A Highly Accurate Multi-Scale Full/Half-Order Polynomial Interpolation
T2  - Computers, Materials \& Continua

PY  - 2011
VL  - 25
IS  - 3
SN  - 1546-2226

AB  - 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 <i>m</i>-order polynomial with a multi-scale technique to interpolate 2<i>m</i>+1 data. Numerical results confirm the validity of present polynomial interpolation method, where only a constant parameter <i>R<sub>0</sub></i> needs to be specified in the multi-scale expansion. For the Differential Quadrature (DQ), the present method provides a very accurate numerical differential. Then, by a combination of this DQ and the Fictitious Time Integration Method (FTIM), we can solve nonlinear boundary value problems effectively.
KW  - Multi-scale polynomial interpolation
KW  -  Half-order polynomial interpolation
KW  -  Differential quadratures
KW  -  Vandermonde matrices

DO  - 10.3970/cmc.2011.025.239