Homework6 - Department of Mathematics University of Houston...

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Department of Mathematics University of Houston Numerical Analysis I Dr. Ronald H.W. Hoppe Numerical Mathematics I (6th Homework Assignment) Exercise 21 ( Regula falsi of higher order ) Assume that f C 1 ([ a,c )) , 0 < a < c, has a simple zero x * [ a,c ] and that f ( a ) f ( c ) < 0. Let b such that a < b < c and consider the quadratic polynomial p P 2 (lR) interpolating f in a,b,c , i.e. p ( z ) = f ( z ) ,z ∈ { a,b,c } . (i) Show that p has exactly one zero in [ a,c ]. (ii) Denote by REAL zero( a,b,c,f ) the function which computes the zero of p for given a,b,c . Using this function, construct an iterative algorithm which provides an approximation of x * up to machine accuracy eps. Exercise 22 ( Newton’s method for the computation of the m -th root ) (i) For m lN, the positive m -th root x * > 0 of a > 0 is the solution of the equation f ( x ) = 0 where f ( x ) := x m - a . Assume
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Homework6 - Department of Mathematics University of Houston...

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