This preview shows pages 1–6. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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 = supδxδ f  / δx If f is differentiable… Click to edit Master subtitle style...
View
Full
Document
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.
 Spring '08
 Staff

Click to edit the document details