= f(x) g(x) dx) Let V = C[-1, 1] under the L² (−1, 1) inner product ((ƒ, g) = (note that this is the real case). Let S = P3 (regarded as a subspace of V) and let f(x) = e. 1. Using the standard basis for S, find the best approximation to f from S. 2. Use the Gram-Schmidt procedure, find an orthogonal basis for S. 3. Use your orthogonal basis to re-compute the answer to the first problem. You are encouraged to use Mathematica, Wolfram Alpha, Matlab, or some other software system to compute the necessary integrals (and to solve the linear system in #1). Otherwise, you re going to be doing a lot of integration by parts! Make a note of where you obtained the values of the integrals. (Even better, do the entire assignment in a Mathematica notebook.)
= f(x) g(x) dx) Let V = C[-1, 1] under the L² (−1, 1) inner product ((ƒ, g) = (note that this is the real case). Let S = P3 (regarded as a subspace of V) and let f(x) = e. 1. Using the standard basis for S, find the best approximation to f from S. 2. Use the Gram-Schmidt procedure, find an orthogonal basis for S. 3. Use your orthogonal basis to re-compute the answer to the first problem. You are encouraged to use Mathematica, Wolfram Alpha, Matlab, or some other software system to compute the necessary integrals (and to solve the linear system in #1). Otherwise, you re going to be doing a lot of integration by parts! Make a note of where you obtained the values of the integrals. (Even better, do the entire assignment in a Mathematica notebook.)
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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![1
Let V = C[-1, 1] under the L² (-1, 1) inner product ((f, g) = f₁ f(x)g(x) dx)
(note that this is the real case). Let S = P3 (regarded as a subspace of V) and let
f(x) = e.
1. Using the standard basis for S, find the best approximation to f from S.
2. Use the Gram-Schmidt procedure, find an orthogonal basis for S.
3. Use your orthogonal basis to re-compute the answer to the first problem.
You are encouraged to use Mathematica, Wolfram Alpha, Matlab, or some other software
system to compute the necessary integrals (and to solve the linear system in #1).
Otherwise, you are going to be doing a lot of integration by parts! Make a note of where
you obtained the values of the integrals. (Even better, do the entire assignment in
a Mathematica notebook.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe15ed467-90ec-4e60-afef-3d3f6119f74d%2Fdad51fc5-d174-4860-bb04-2ecd82de7119%2Fu6nfbh_processed.png&w=3840&q=75)
Transcribed Image Text:1
Let V = C[-1, 1] under the L² (-1, 1) inner product ((f, g) = f₁ f(x)g(x) dx)
(note that this is the real case). Let S = P3 (regarded as a subspace of V) and let
f(x) = e.
1. Using the standard basis for S, find the best approximation to f from S.
2. Use the Gram-Schmidt procedure, find an orthogonal basis for S.
3. Use your orthogonal basis to re-compute the answer to the first problem.
You are encouraged to use Mathematica, Wolfram Alpha, Matlab, or some other software
system to compute the necessary integrals (and to solve the linear system in #1).
Otherwise, you are going to be doing a lot of integration by parts! Make a note of where
you obtained the values of the integrals. (Even better, do the entire assignment in
a Mathematica notebook.)
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