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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
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.]
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.
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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