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 Document
Unformatted text preview: Michael T. Heath Scientiﬁc Computing 10 / 55 Nonlinear Equations Numerical Methods in One Dimension Methods for Systems of Nonlinear Equations Nonlinear Equations Solutions and Sensitivity Convergence Sensitivity and Conditioning Michael T. Heath Scientiﬁc Computing 11 / 55 Nonlinear Equations Numerical Methods in One Dimension Methods for Systems of Nonlinear Equations Nonlinear Equations Solutions and Sensitivity Convergence Sensitivity and Conditioning What do we mean by approximate solution ˆ x to nonlinear system, k f (ˆ x ) k ≈ or k ˆ xx * k ≈ 0 ? First corresponds to “small residual,” second measures closeness to (usually unknown) true solution x * Solution criteria are not necessarily “small” simultaneously Small residual implies accurate solution only if problem is wellconditioned Michael T. Heath Scientiﬁc Computing 12 / 55...
View
Full Document
 Spring '08
 staff
 Numerical Analysis, Nonlinear system, nonlinear equations, Systems of Nonlinear Equations

Click to edit the document details