Determine Newton's Finite Divided Difference interpolating polynomial for the function values tabulated below as follows: (a) Construct the Finite Divided Difference table in the tabular format of Fig. 18.5. • (b) Using the results of (a) and the tabulated values on the left, determine Newton's Finite Divided Difference interpolating polynomial of order 3, f3(x), (cubic polynomial). • (c) Interpolate the value of the function, f(x), at x = 1.5. (d) Using the polynomial found in (b), estimate analytically the area under the function, f(x), between ro = 1 and x,= 3. • (e) Estimate the same area using the appropriate Simpson's rule. Briefly comment on and explain the results obtained in (d) and (e). • (f) Determine the error of the interpolated value determined in (c) using an additional function value at x4 = -1 : f (x.) = -62. What conclusion can you draw from the result of (f) regarding the order, n, of the polynomial, f(x)=fn(x), used to generate these I; f(r.) 1 4 3 6. -15 function values? 7. 1.

Determine Newton's Finite Divided Difference interpolating polynomial for the function values tabulated below as follows: (a) Construct the Finite Divided Difference table in the tabular format of Fig. 18.5. • (b) Using the results of (a) and the tabulated values on the left, determine Newton's Finite Divided Difference interpolating polynomial of order 3, f3(x), (cubic polynomial). • (c) Interpolate the value of the function, f(x), at x = 1.5. (d) Using the polynomial found in (b), estimate analytically the area under the function, f(x), between ro = 1 and x,= 3. • (e) Estimate the same area using the appropriate Simpson's rule. Briefly comment on and explain the results obtained in (d) and (e). • (f) Determine the error of the interpolated value determined in (c) using an additional function value at x4 = -1 : f (x.) = -62. What conclusion can you draw from the result of (f) regarding the order, n, of the polynomial, f(x)=fn(x), used to generate these I; f(r.) 1 4 3 6. -15 function values? 7. 1.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section4.3: Zeros Of Polynomials

Problem 66E

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