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Let 2₁, 22, ..., 2 be distinct complex numbers. We define the ith Lagrange polynomial to be and note immediately that P:(2) = II 2-2; 2₁-2; Pi(2j) = díj, where §¡¡ is the Kronecker delta. We now observe that if P(2) is any polynomial of Hegree less than or equal to (k − 1), we have the following representation for P(2): P(2) = Σ P{(^)P(2₂), i=1

Let 2₁, 22, ..., 2 be distinct complex numbers. We define the ith Lagrange polynomial to be and note immediately that P:(2) = II 2-2; 2₁-2; Pi(2j) = díj, where §¡¡ is the Kronecker delta. We now observe that if P(2) is any polynomial of Hegree less than or equal to (k − 1), we have the following representation for P(2): P(2) = Σ P{(^)P(2₂), i=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 2₁, 22, ..., 2 be distinct complex numbers. We define the ith Lagrange polynomial to be and note immediately that Pi(2) = II j=12₁-2₂ Pi(2j) = díj, where 8, is the Kronecker delta. We now observe that if P(2) is any polynomial of degree less than or equal to (k − 1), we have the following representation for P(2): P(2) = Σ P:{(2)P(2), i=1
Transcribed Image Text:Let 2₁, 22, ..., 2 be distinct complex numbers. We define the ith Lagrange polynomial to be and note immediately that Pi(2) = II j=12₁-2₂ Pi(2j) = díj, where 8, is the Kronecker delta. We now observe that if P(2) is any polynomial of degree less than or equal to (k − 1), we have the following representation for P(2): P(2) = Σ P:{(2)P(2), i=1
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