On P(R), consider the inner product given by 1 (p · q) = ["'p(x)q(x) dx. Apply the Gram-Schmidt Procedure to the basis 1, x, x² to produce an ortho- normal basis of P(R).
On P(R), consider the inner product given by 1 (p · q) = ["'p(x)q(x) dx. Apply the Gram-Schmidt Procedure to the basis 1, x, x² to produce an ortho- normal basis of P(R).
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:On P(R), consider the inner product given by
1
(p.q)
["P(x)
0
Apply the Gram-Schmidt Procedure to the basis 1, x, x² to produce an ortho-
normal basis of P(R).
=
p(x)q(x) dx.
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