CIS 541 – Numerical Methods Roger Crawfis Ohio State University CIS 541 – Numerical Methods Root Finding August 12, 2005 OSU/CIS 541 3 Root Finding Topics • Bi-section Method • Newton’s method • Uses of root finding for sqrt() and reciprocal sqrt() • Secant Method • Generalized Newton’s method for systems of non- linear equations – The Jacobian matrix • Fixed-point formulas, Basins of Attraction and Fractals. August 12, 2005 OSU/CIS 541 4 Motivation • Many problems can be re-written into a form such as: – f(x,y,z,…) = 0 – f(x,y,z,…) = g(s,q,…)
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