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
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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
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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