Problem 5. Consider the inner product space from Problem 1. Let V be the sub- space spanned by the functions h₁(x) = 1 and h₂(x) = 2x - 1. Find the best least squares approximation to the function f(x)=√ on [0, 1] by a function from V. [Hint: first show that h₁ and h₂ are orthogonal.]
Problem 5. Consider the inner product space from Problem 1. Let V be the sub- space spanned by the functions h₁(x) = 1 and h₂(x) = 2x - 1. Find the best least squares approximation to the function f(x)=√ on [0, 1] by a function from V. [Hint: first show that h₁ and h₂ are orthogonal.]
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 5 with information of problem 1
![Problem 5. Consider the inner product space from Problem 1. Let V be the sub-
space spanned by the functions h₁(x) = 1 and h₂(x) = 2x - 1. Find the best least squares
approximation to the function f(x)=√ on [0, 1] by a function from V.
[Hint: first show that h₁ and h₂ are orthogonal.]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F47d370c3-9e4b-442d-9a89-d591c5ced338%2F07c1e878-7bdb-4434-a7f6-22db32fe13db%2F557kclv_processed.png&w=3840&q=75)
Transcribed Image Text:Problem 5. Consider the inner product space from Problem 1. Let V be the sub-
space spanned by the functions h₁(x) = 1 and h₂(x) = 2x - 1. Find the best least squares
approximation to the function f(x)=√ on [0, 1] by a function from V.
[Hint: first show that h₁ and h₂ are orthogonal.]
![Problem 1. Consider the inner product space C[0, 1] with the inner product defined by
(f.g) = f* f(x)g(x) dx
and the induced norm. Find the angle between the functions h₁(x) = 1 and h₂(x) =
= x.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F47d370c3-9e4b-442d-9a89-d591c5ced338%2F07c1e878-7bdb-4434-a7f6-22db32fe13db%2Fhdrryy_processed.png&w=3840&q=75)
Transcribed Image Text:Problem 1. Consider the inner product space C[0, 1] with the inner product defined by
(f.g) = f* f(x)g(x) dx
and the induced norm. Find the angle between the functions h₁(x) = 1 and h₂(x) =
= x.
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