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Lecture 3: Solving Equations Using Fixed Point Iterations

Cs412: introduction to numerical analysis09/14/10 Lecture 3: Solving Equations Using Fixed Point IterationsInstructor: Professor Amos Ron Scribes: Yunpeng Li, Mark Cowlishaw, Nathanael FillmoreOur problem, to recall, is Solving Equations in one variable. We are given a functionf, andwould like to find at least one solution to the equationf(x) = 0. Note that,a priori, we do notput any restrictions on the functionf; we do need to be able to evaluate the function: otherwise,we cannot even check that a given solutionx=ris true, , thatf(r) = 0. In reality, the mereability to be able to evaluate the function does not suffice. Weneed to assume some kind of goodbehavior . The more we assume, the more potential we have, onthe one hand, to develop fastalgorithms for finding the root.

Lecture 3: Solving Equations Using Fixed Point Iterations Instructor: Professor Amos Ron Scribes: Yunpeng Li, Mark Cowlishaw, Nathanael Fillmore Our problem, to recall, is solving equations in one variable. We are given a function f, and ... convergence, we can take the ratio ...

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