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Root Finding Algorithm: Analysis, Deficiencies, & Benefits

Explore the results and analysis of a root-finding algorithm with xl, xm, and xr values, noting convergence issues and benefits. Learn why the method converges slowly and may fail in certain instances, such as when the initial bounds enclose two roots. Discover the lecture material on void functions with changing arguments, highlighting the reliability of the algorithm in certain scenarios.

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Root Finding Algorithm: Analysis, Deficiencies, & Benefits

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  1. Results xl xm xr f(xl) f(xm) f(xr) 2 4 6 -3.56 -3.48 9.88 4 5 6 -3.48 1.00 9.88 4 4.5 5 -3.48 -1.7225 1.00 4.5 4.75 5 -1.7225 -.49031 1.00 4.75 4.875 5 -.49031 .221523 1.00 4.75 4.8125 4.875 -.49031 -.14259 .221523 ……. 17th step = 4.83728 4.83731 4.83734 -.0002 -.000026 .000151 Deficiencies : Converges slowly May not work if initial bounds surround two roots Benefits: Reliable Lecture 10 Void functions with changing arguments

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