Lagrange interpolation
2016-08-23
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In the given node on a node basis functions and linear combinations of basis functions, constant values for a node, the interpolation polynomial is called the Lagrange interpolation formula
Linear interpolation is also called two-point interpolation, known function y = f (x) given distinct points x0, X1 has a value of Y0= f (x0), y1=f (X1), linear interpolation is to construct a polynomial
P1(x) = ax + b
Make it satisfy the condition
P1 (x0) = y0 P1 (x1) = y1
The geometric interpretation is a straight line through points a known (x0, y0), b (X1, y1).
Linear interpolation calculation purposes, the application is very broad, but because it is in a straight line instead of a curve, thus General requirements [x0, X1] is relatively small, and f (x) [x0, X1] changes smoothly, otherwise the error of linear interpolation can be quite large. In order to overcome this shortcoming, sometimes with a simple curve to approximately replace the complex cu
P1(x) = ax + b
Make it satisfy the condition
P1 (x0) = y0 P1 (x1) = y1
The geometric interpretation is a straight line through points a known (x0, y0), b (X1, y1).
Linear interpolation calculation purposes, the application is very broad, but because it is in a straight line instead of a curve, thus General requirements [x0, X1] is relatively small, and f (x) [x0, X1] changes smoothly, otherwise the error of linear interpolation can be quite large. In order to overcome this shortcoming, sometimes with a simple curve to approximately replace the complex cu
matlab
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lagrange
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