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IV. USE OF NEWTON FORWARD AND BACKWARD INTERPOLATION METHOD Forward interpolation formula is used to interpolate the values of y nearer to the beginning value of the given table. Also this formula is applicable if in case where h (difference in in travel) is constant. Now coming to backward difference formula. [1]

17.10.2017 · Newton Forward And Backward Interpolation. Interpolation is the technique of estimating the value of a function for any intermediate value of the independent variable, while the process of computing the value of the function outside the given range is called extrapolation. Forward Differences: The differences y1 – y0, y2 – y1, y3 – y2 ...

Gauss forward formula is derived from Newton’s forward formula which is: Newton’s forward interpretation formula: Yp=y0+p.Δy0+ p(p-1)Δ2y0/(1.2) + p(p-1)(p-2)Δ3y0/(1.2.3)+….

= 1. [(x1 - x)f0 + (x-x0)f1]. (x1 - x0) ; f(x) @ Pn(x) = f0 + rDf0 +. r(r-1). D2f · + . . . +. r(r-1) . . . (r - n +1). Dnf · 2! ; f(x) = f0 + rDf0 +. r(r-1). D2f ...

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This formula is useful when the value of f(x) is required near the end of the table. h is called the interval of difference and u = ( x – an ) / ...

Newton's backward interpolation formula. #. Central difference interpolation formulae. #. Gauss's forward interpolation formula.

IV. USE OF NEWTON FORWARD AND BACKWARD INTERPOLATION METHOD Forward interpolation formula is used to interpolate the values of y nearer to the beginning value of the given table. Also this formula is applicable if in case where h (difference in in travel) is constant. Now coming to backward difference formula. [1]

These interpolation formulae are applicable for interpretation near the beginning and end of tabulated values. However, the gaussian forward formula are best suited for interpolation near the middle of the table. The coefficients in the central difference formula such as that of gauss are smaller and converge faster than those in Newton's formulae.

NEWTON BACKWARD INTERPOLATION FORMULA Taking p = h x x n, we get the interpolation formula as: P(x n +ph) = y 0 + p y n + 2! p(p 1) 2y n + 3! p(p 1)(p 2) 3y n + / + n! p (p 1) (p 2) } (p n 1) ny n ENGINEERING MATHEMATICS III

dyn–1 are respectively, called the first forward differences. II. NEWTON'S GREGORY FORWARD. INTERPOLATION METHOD. This formula is mainly useful for ...

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NEWTON BACKWARD INTERPOLATION FORMULA Taking p = h x x n, we get the interpolation formula as: P(x n +ph) = y 0 + p y n + 2! p(p 1) 2y n + 3! p(p 1)(p 2) 3y n + / + n! p (p 1) (p 2) } (p n 1) ny n ENGINEERING MATHEMATICS III

Gregory-Newton or Newton Forward Difference Interpolation P(x0+hs)=f0+sΔf0+s(s−1)2!Δ2f0+⋯+s(s−1)(s−2)...(s−n+1)n!Δnf0 · Gregory-Newton or Newton Backward ...

Thus the first forward differences are. : NEWTON'S GREGORY FORWARD INTERPOLATION FORMULA : This formula is particularly useful for interpolating the values of f ...

y(x)=y0+pΔy0+p(p-1)2!⋅Δ2y0+p(p-1)(p-2)3!⋅Δ3y0+p(p-1)(p-2)(p-3)4!⋅Δ4y0+...

Remark 11.4.3 If the interpolating point lies closer to the beginning of the interval then one uses the Newton's forward formula and if it lies towards the end ...

Oct 17, 2017 · u = (value - x [ 0 ]) / (x [ 1] - x [ 0 ]); for i in range ( 1 ,n): sum = sum + (u_cal (u, i) * y [ 0 ] [i]) / fact (i); print ( " Value at", value, "is", round ( sum, 6 )); # This code is contributed by mits. C#. // C# Program to interpolate using. // newton forward interpolation.