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CSC fll Fortran Project Spring 2010 Iy'th Roots 1 Introduction and Due Date An algorithm for finding a square root of a given real number, N, to a...

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Fortran Project Iy'th Roots 1 Introduction and Due Date An algorithm for finding a square root of a given real number, N, to a given level, limit, of accuracy is well known' It is called the Newton-Riphson algorithm. with ; httle math, it can easily be modified to find the nth root of a number, too. The compilers on taz are f95 and gfortran _ use either one. tr'or help with Fortran, refer to any Fortran text or look on the web. There is also a brief ,,manual,, in my directory /hone/UnlClasses/Cscl/Fo rtran/ on taz. This assignment is due on: Monday, vrarctr;filt the start of ciass. There is no need for a formal report. 2 The Algorithm we begin by "guessing" the answer; let o-ur guess be G. G islikely to be incorrec t; Iet G : t/N + 6. Therefore, doing the division , N-LG : vN _*d + . ., i.e. wk = JN _a. li *" _rerpo.late between G(orfN*d) and lvp(or\/N- d),weget,roughly,\/Iv,-1;'"";""r","'*"ethatiscloser to the true value of t/N than was G, which becomes our next ,,guess,,, l/G If we continue in this way' we can get arbitrarily close to the correct value; i.e., to within limit of the correct value. An acceptable value for the initial guess is L.0. CSC fll What to Do Spring 2010 (A) code the square root algorithm with limit set to 0.0005. Modify the algorithm so that the output includes the number of guesses that were made. Run it on u*u"tiy the numbers 0.5, 1.0, 100.0, 1b0.00, 5000.0 and 62632.82. (B) Examine the math behind the square root algorithm and use it to develop an analogous algorithm (including the outputting of the nuniber of guesses made) to find 'tlF (';;"g"o,"; N real). (Hint: interpoiate between the guess, c, uri wyc,,-r.In computing G,-1, use a loop, not the ex-p functjon.) use that algorithm, with limit:0.0005, to hnd exactly Vnn, {n;sr, in4'.o, arrd ylnt23. What to Ttrrn In 1. A iisting of the source code and the run in (A). 2. The math (pen and paper is okay) used to develop the itself. 3. A listing of the source code and the run in (B). algorithm in (B) and the algorithm
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