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1.4 Newton-Raphson and Secant Methods

1.4 Newton-Raphson and Secant Methods. 1.4.1 Slope Methods for Finding Roots. 1.4.2 The Division-by-Zero Error. 1.4.3 Speed of Convergence. 1.4.4 Pitfalls. 1.4.5 Secand Method. 1.4.6 Accelerated Convergence.

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XM=(XL+XR)/2

The mechanics of Newton, Bi-section, and Secant methods. Use 3 its of Newton to fine the root of f(X)=X 2 -3 near X =1. X=Xold +( -F/Fdash). Use 3 its of Bi-section to fine the root of f(X)=X 2 -3 between X =1 and X=2. XM=(XL+XR)/2.

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Secant method table

Secant method table. f(xn-1). xn-1. xn. f(xn). xn+1. n. 1. 4.0000. -3.4800. 6.0000. 9.8800. 4.5210. 4.7303. 9.8800. 2. 6.0000. 4.5210. -1.6287. -1.6287. 3. 4.7303. -0.5967. 4.8513. 4.5210. 4.8368. -0.5967. -0.0815. 4.8513. 4.7303. 4. -.0032. 5. 4.8513. 4.8373.

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Secant methods - PowerPoint PPT Presentation

1.4 Newton-Raphson and Secant Methods

XM=(XL+XR)/2

Secant method table