Let , a closed interval, and satisfies a local requirements on The I g I. theorem’s Taylor series of about is g x=s = = , where = . If , and , then convergence. kthorder The important are 1 and 2. k’s If we only have 1st order convergence, we can speed it up using quadratic interpolation: given , fit a 2nd order polynomial to the data such that . Use to p p get the next guess. Let
Let , I a closed interval, and g satisfies a local theorem’s requirements on I. The Taylor series of g about x=s is = = , where = . If , and , then kthorder convergence. The important k’s are 1 and 2. If we only have 1st order convergence, we can speed it up using quadratic interpolation: given , fit a 2nd order polynomial p to the data such that . Use p to get the next guess. Let
2013sw.docx