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Prove that there is only one polynomial P3(x) among all polynomials of degree < 3 that satisfy the interpolating conditions 11. (а) P3(x;) = yi, i = 0, 1, 2, 3 where the x;'s are distinct. Hint: Generalize the proof given in and following (4.10) for the uniqueness of P2(x). (b) Give a proof of uniqueness for P(x) in Theorem 4.1.5.

Prove that there is only one polynomial P3(x) among all polynomials of degree < 3 that satisfy the interpolating conditions 11. (а) P3(x;) = yi, i = 0, 1, 2, 3 where the x;'s are distinct. Hint: Generalize the proof given in and following (4.10) for the uniqueness of P2(x). (b) Give a proof of uniqueness for P(x) in Theorem 4.1.5.

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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11. (а) Prove that there is only one polynomial P3(x) among all polynomials of degree < 3 that satisfy the interpolating conditions P3(x;) = = yi, i = 0, 1, 2, 3 where the x;'s are distinct. Hint: Generalize the proof given in and following (4.10) for the uniqueness of P2(x). (b) Give a proof of uniqueness for P(x) in Theorem 4.1.5.
Transcribed Image Text:11. (а) Prove that there is only one polynomial P3(x) among all polynomials of degree < 3 that satisfy the interpolating conditions P3(x;) = = yi, i = 0, 1, 2, 3 where the x;'s are distinct. Hint: Generalize the proof given in and following (4.10) for the uniqueness of P2(x). (b) Give a proof of uniqueness for P(x) in Theorem 4.1.5.
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