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Problem 1: Here is a set of polynomials {1,1-x}. Is this a linearly independent or dependent set, and why? Show that this collection of polynomials is orthogonal with respect to the weight function w(x) = exp(-x) on (0, ∞). Show your working, you should not just plug integrals in to a software-solver. (c) Hence find the least squares polynomial P(x) = aogo(x) + aigi(x) for f(x) = e, where {go(x), g1(x)} = {1,1-x}. Show your workings. (a) (b)

Problem 1: Here is a set of polynomials {1,1-x}. Is this a linearly independent or dependent set, and why? Show that this collection of polynomials is orthogonal with respect to the weight function w(x) = exp(-x) on (0, ∞). Show your working, you should not just plug integrals in to a software-solver. (c) Hence find the least squares polynomial P(x) = aogo(x) + aigi(x) for f(x) = e, where {go(x), g1(x)} = {1,1-x}. Show your workings. (a) (b)

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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Numerical Analysis

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Problem 1: Here is a set of polynomials {1,1-x}. Is this a linearly independent or dependent set, and why? Show that this collection of polynomials is orthogonal with respect to the weight function w(x) = exp(-x) on (0, ∞). Show your working, you should not just plug integrals in to a software-solver. (c) Hence find the least squares polynomial P(x) = aogo(x) + aigi(x) for f(x) = e, where {go(x), g1(x)} = {1,1-x}. Show your workings. (a) (b)
Transcribed Image Text:Problem 1: Here is a set of polynomials {1,1-x}. Is this a linearly independent or dependent set, and why? Show that this collection of polynomials is orthogonal with respect to the weight function w(x) = exp(-x) on (0, ∞). Show your working, you should not just plug integrals in to a software-solver. (c) Hence find the least squares polynomial P(x) = aogo(x) + aigi(x) for f(x) = e, where {go(x), g1(x)} = {1,1-x}. Show your workings. (a) (b)
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