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Rootfinding for Nonlinear Equations

> 3. Rootfinding Rootfinding for Nonlinear Equations 3. Rootfinding Math 1070. > 3. Rootfinding Calculating the roots of an equation f (x) = 0 ( ). is a common problem in applied mathematics. We will explore some simple numerical methods for solving this equation, and also will consider some possible difficulties 3. Rootfinding Math 1070. > 3. Rootfinding The function f (x) of the equation ( ). will usually have at least one continuous derivative, and often we will have some estimate of the root that is being sought. By using this information, most numerical methods for ( ) compute a sequence of increasingly accurate estimates of the root.

5 1.1250 1.1875 1.1562 0.0312 0.2333 6 1.1250 1.1562 1.1406 0.0156 0.0616 7 1.1250 1.1406 1.1328 0.0078 -0.0196 8 1.1328 1.1406 1.1367 0.0039 0.0206 9 1.1328 1.1367 1.1348 0.0020 0.0004 10 1.1328 1.1348 1.1338 0.00098 -0.0096 Table: Bisection Method for (7.3) The entry nindicates that the associated row corresponds to iteration number nof steps ...

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