Let P0. (x) denote the quadratic polynomial that interpolates the data {(xo, yo), (x1, y1), (x2, y2)}; let P"(x) denote the quadratic polynomial that interpolates the data {(x1, yi), (x2, y2), (x3, y3)}. Finally, let P3(x) de- note the cubic polynomial interpolating the data {(xo, yo), (x1, yı), (x2, y2), (x3, y3)}. Show that 14. (a) (x3 – x)P0. (x) + (x – xo)P{t.) (x) P3(x) = X3 - x0 (b) How might this be generalized to constructing Pn(x), interpolating {(xo, yo), (x.. Yu)}, from interpolation polynomials of degree n – 1?

Let P0. (x) denote the quadratic polynomial that interpolates the data {(xo, yo), (x1, y1), (x2, y2)}; let P"(x) denote the quadratic polynomial that interpolates the data {(x1, yi), (x2, y2), (x3, y3)}. Finally, let P3(x) de- note the cubic polynomial interpolating the data {(xo, yo), (x1, yı), (x2, y2), (x3, y3)}. Show that 14. (a) (x3 – x)P0. (x) + (x – xo)P{t.) (x) P3(x) = X3 - x0 (b) How might this be generalized to constructing Pn(x), interpolating {(xo, yo), (x.. Yu)}, from interpolation polynomials of degree n – 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 65E

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