Transcription of Lecture 8 : Fixed Point Iteration Method, Newton’s Method
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Lecture 8 : Fixed Point Iteration Method, Newton’s Method
1 Lecture 8 : Fixed Point Iteration Method , Newton s MethodIn the previous two lectures we have seen some applications of the mean value theorem. We nowsee another this Lecture we discuss the problem of finding approximate solutions of the equationf(x) = 0.(1)In some cases it is possible to find the exact roots of the equation (1), for example, whenf(x) isa quadratic or cubic polynomial. Otherwise, in general, one is interested in finding approximatesolutions using some (numerical) methods . Here, we will discuss a Method called Fixed pointiteration Method and a particular case of this Method called Newton s Point Iteration Method :In this Method , we first rewrite the equation (1) in the formx=g(x)(2)in such a way that any solution of the equation (2), which
iteration method and a particular case of this method called Newton’s method. Fixed Point Iteration Method : In this method, we flrst rewrite the equation (1) in the form x = g(x) (2) in such a way that any solution of the equation (2), which is a flxed point of g, is a solution of equation (1). Then consider the following algorithm ...
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