251 Lecture 12 Condition

251 Lecture 12 Condition - Click to edit Master subtitle...

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Unformatted text preview: Click to edit Master subtitle style 4/14/11 Conditioning and Stability Conditioning : Small perturbation in input makes large change in function. Stability : Small perturbation in input makes a large change in the result of the method to compute the function Click to edit Master subtitle style 4/14/11 Conditioning and Stability Conditioning : Small perturbation in input makes large change in function. - SVD Stability : Small perturbation in input makes a large change in the result of the method to compute the function – Gram Schmidt Click to edit Master subtitle style 4/14/11 Conditioning Conditioning : Small perturbation in input makes large change in function. Well – conditioned f (xi) = yi& f (xi+ δ) = yi + ε Ill – conditioned f (xi) = yi& f (xi+ δ) = yi + M Where δ and ε are small, and M is large Click to edit Master subtitle style 4/14/11 Conditioning Conditioning : Small perturbation in input makes large change in function. Well – conditioned f (xi) = yi& f (xi+ δ) = yi + ε Ill – conditioned f (xi) = yi& f (xi+ δ) = yi + M Chaos : where δ and ε are small, and M is unpredictable (uncomputable) Click to edit Master subtitle style 4/14/11 Conditioning Conditioning number Let δ f = f (x+ δx) - f (x) Then for infinitesimal δx the absolute condition number is κ = supδx||δ f || / ||δx|| If f is differentiable… Click to edit Master subtitle style...
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This note was uploaded on 04/13/2011 for the course CSCE 211 taught by Professor Staff during the Spring '08 term at Columbia SC.

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251 Lecture 12 Condition - Click to edit Master subtitle...

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