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# Chap2 - NUMERICAL ANALYSIS AAOC C341 CHAPTER 2 Root Finding...

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1 NUMERICAL ANALYSIS AAOC C341 CHAPTER 2 Root Finding Methods for Nonlinear Equations

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2 Root Finding Methods for Nonlinear Equations Bisection Method Secant Method Regula-Falsi Method Newton’s Method Muller’s Method Fixed Point Method Newton’s Method for Multiple Roots System of Non-linear Equations Newton’s Method and Fixed Point Method
3 Introduction: In scientific and engineering studies, a frequently occurring problem is to find the roots or zeros of equations of the form f(x) =0 . f(x) may be algebraic or transcendental or a combination of both. Algebraic functions of the form P(x)= a 0 + a 1 x + … + a n x n , are called polynomials . A non-algebraic function is called a transcendental function.

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4 Solution Methods Polynomials up to degree 4 can be solved exactly. Since finding the root of f(x)=0 is not always possible by analytical means, we have to go for some other techniques or methods. Solution Methods are either Bracketing: Bisection Method, Regula Falsi Method or Iterative: Secant Method, Newton's Method, Muller's Method, Fixed-Point Method. Rate of Convergence. Advantages/Disadvantages.