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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?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Let P0" (x) denote the quadratic polynomial that interpolates the data {(xo, yo), (x1, yı), (x2, y2)}; let P"."(x) denote the quadratic polynomial that interpolates the data {(x1, yı), (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)P0.2) (x) + (x – xo) P!.3) (x) P3 (x) = (1,3) X3 - Xo How might this be generalized to constructing P(x), interpolating {(xo, yo), (Xn, Yn)}, from interpolation polynomials of degreen – 1? (b) ....
Transcribed Image Text:Let P0" (x) denote the quadratic polynomial that interpolates the data {(xo, yo), (x1, yı), (x2, y2)}; let P"."(x) denote the quadratic polynomial that interpolates the data {(x1, yı), (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)P0.2) (x) + (x – xo) P!.3) (x) P3 (x) = (1,3) X3 - Xo How might this be generalized to constructing P(x), interpolating {(xo, yo), (Xn, Yn)}, from interpolation polynomials of degreen – 1? (b) ....
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