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Find the function of the form y = + ₁ sin(πx) + c₂ cos(TX) that best fits the data in the following table in a weighted least squares sense; that is, minimize Σ½-1 W; (Yi — Co – c₁ sin(π£;) — c₂ cos(π£;))², where w = =W3 = 1 and W2 =W₁ = 2. a) Set up the least squares problem to be solved in the form Ax≈ b. x y 01 0.5 2 10 1.5 -2

Find the function of the form y = + ₁ sin(πx) + c₂ cos(TX) that best fits the data in the following table in a weighted least squares sense; that is, minimize Σ½-1 W; (Yi — Co – c₁ sin(π£;) — c₂ cos(π£;))², where w = =W3 = 1 and W2 =W₁ = 2. a) Set up the least squares problem to be solved in the form Ax≈ b. x y 01 0.5 2 10 1.5 -2

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.3: Least Squares Approximation
Problem 32EQ
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Find the function of the form y = c + ₁ sin(πx) + c₂ cos(TX) that best fits the data in the following table in a weighted least squares sense; that is, minimize Σ₁₁ W; (y₁ − c - c₁ sin(πx;) — c₂ cos(πx;))², where w W3 = 1 and W₂ = W4 = 2. = a) Set up the least squares problem to be solved in the form Ax≈ b. x y 0 1 0.5 2 1 0 1.5 -2
Transcribed Image Text:Find the function of the form y = c + ₁ sin(πx) + c₂ cos(TX) that best fits the data in the following table in a weighted least squares sense; that is, minimize Σ₁₁ W; (y₁ − c - c₁ sin(πx;) — c₂ cos(πx;))², where w W3 = 1 and W₂ = W4 = 2. = a) Set up the least squares problem to be solved in the form Ax≈ b. x y 0 1 0.5 2 1 0 1.5 -2
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