Problem 8. Consider the inner product space from Problem 4. Find an orthonormal basis for the subspace of C[-1,1] spanned by functions h₁(x) = 1, h₂(x) = x and h3(x) = x².
Problem 8. Consider the inner product space from Problem 4. Find an orthonormal basis for the subspace of C[-1,1] spanned by functions h₁(x) = 1, h₂(x) = x and h3(x) = x².
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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Please solve problem 8 with reference to problem 4
![Problem 4. Consider the inner product space C[-1, 1] with the inner product defined by
(f,g) =
f(x)g(x) dx
and the induced norm. Find the best least squares approximation to the function f(x) = x¹/³
on [-1, 1] by a linear function ((x) = ₁ + ₂x.
[Hint: first show that the functions h₁(x) = 1 and h₂(x) = x are orthogonal.]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F47d370c3-9e4b-442d-9a89-d591c5ced338%2F423d7a42-0f69-4189-ad60-fecfd5020e7c%2Fv5jzmzl_processed.png&w=3840&q=75)
Transcribed Image Text:Problem 4. Consider the inner product space C[-1, 1] with the inner product defined by
(f,g) =
f(x)g(x) dx
and the induced norm. Find the best least squares approximation to the function f(x) = x¹/³
on [-1, 1] by a linear function ((x) = ₁ + ₂x.
[Hint: first show that the functions h₁(x) = 1 and h₂(x) = x are orthogonal.]
![Problem 8. Consider the inner product space from Problem 4. Find an orthonormal
basis for the subspace of C[-1,1] spanned by functions h₁(x) = 1, h₂(x) = x and h3(x) = x².](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F47d370c3-9e4b-442d-9a89-d591c5ced338%2F423d7a42-0f69-4189-ad60-fecfd5020e7c%2Fbu54au_processed.png&w=3840&q=75)
Transcribed Image Text:Problem 8. Consider the inner product space from Problem 4. Find an orthonormal
basis for the subspace of C[-1,1] spanned by functions h₁(x) = 1, h₂(x) = x and h3(x) = x².
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