Transcription of Lecture 3: Solving Equations Using Fixed Point Iterations
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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.
numeric solution r. In a previous lecture, we introduced an iterative process for finding roots of quadratic equations. We will now generalize this process into an algorithm for solving equations that is based on the so-called fixed point iterations, and therefore is referred to as fixed point algorithm. In order to use fixed point ...
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