High-Order Polynomial Interpolation Based on the Interpolation Center's Neighborhood The Amendment to the Runge Phenomenon

High-order interpolation polynomial has better approximation to its original function near the interpolation center than low-order polynomial but will arise Runge phenomenon near the border of the interpolation area; while low-order interpolation polynomial has large error in the whole interpolation area. This article used high-order polynomial interpolation based on the interpolation center's neighborhood to do high-order polynomial interpolation in the whole interpolation area, got the better approximation to the original function, and amended the Runge phenomenon effectively.