So far we have considered the construction of a polynomial, which approximates a given function and takes the same values as the function at certain given points. This is called the method of collocation and the conditions are satisfied by the approximate Lagrange’s interpolation polynomial. When the given points are equally spaced, we can form a difference table and find the polynomial using Newton’s forward difference formula. For example, the polynomial 4*x* – 4*x*^{2} agrees with the function sin *π**x* for but this approximation is not very satisfactory because the polynomial 4*x* – 4*x*^{2} is larger than sin *π**x* in the range (0,1) except ...

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