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(a) Prove that if p is a polynomial of degree at most n and To,. ,In are distinct nodes 72 Σlj(x)p(x) = p(x), j=0 (1) where the l, (x) are the elementary Lagrange polynomials associated with the nodes To,, In. (b) Prove that n Σι; (x) = 1. j=0 (2)

(a) Prove that if p is a polynomial of degree at most n and To,. ,In are distinct nodes 72 Σlj(x)p(x) = p(x), j=0 (1) where the l, (x) are the elementary Lagrange polynomials associated with the nodes To,, In. (b) Prove that n Σι; (x) = 1. j=0 (2)

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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number analysis practice question,Please write the simplest answer process,thanks.
(a) Prove that if p is a polynomial of degree at most n and To,..., In are distinct nodes 72 Σι;(x)p(x;) = p(x), j=0 where the l; (x) are the elementary Lagrange polynomials associated with the nodes To,, In- (b) Prove that n (1) Σι;(x) = 1. j=0 (2)
Transcribed Image Text:(a) Prove that if p is a polynomial of degree at most n and To,..., In are distinct nodes 72 Σι;(x)p(x;) = p(x), j=0 where the l; (x) are the elementary Lagrange polynomials associated with the nodes To,, In- (b) Prove that n (1) Σι;(x) = 1. j=0 (2)
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