Linear Algebra and Its Applications · Problem 3.3.38

Orthogonality — Gilbert Strang

Mathematics · weighted-least-squares

Problem

What happens to the weighted average x^W=(w12b1+w22b2)/(w12+w22)\hat{x}_W = (w_1^2 b_1 + w_2^2 b_2)/(w_1^2 + w_2^2) if the first weight w1w_1 approaches zero? The measurement b1b_1 is totally unreliable.

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