How to resolve the algorithm Arithmetic-geometric mean step by step in the PL/I programming language

Published on 12 May 2024 09:40 PM
#Pl/i

How to resolve the algorithm Arithmetic-geometric mean step by step in the PL/I programming language

Table of Contents

Problem Statement

Write a function to compute the arithmetic-geometric mean of two numbers.

The arithmetic-geometric mean of two numbers can be (usefully) denoted as

a g m

( a , g )

{\displaystyle \mathrm {agm} (a,g)}

, and is equal to the limit of the sequence: Since the limit of

a

n

−

g

n

{\displaystyle a_{n}-g_{n}}

tends (rapidly) to zero with iterations, this is an efficient method. Demonstrate the function by calculating:

Let's start with the solution:

Step by Step solution about How to resolve the algorithm Arithmetic-geometric mean step by step in the PL/I programming language

Source code in the pl/i programming language

arithmetic_geometric_mean:           /* 31 August 2012 */
   procedure options (main);
   declare (a, g, t) float (18);

   a = 1; g = 1/sqrt(2.0q0);
   put skip list ('The arithmetic-geometric mean of ' || a || ' and ' || g || ':');
   do until (abs(a-g) < 1e-15*a);
      t = (a + g)/2; g = sqrt(a*g);
      a = t;
      put skip data (a, g);
   end;
   put skip list ('The result is:', a);
end arithmetic_geometric_mean;

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