| ??? 07/07/05 06:40 Read: times |
#96752 - square root by newtons method Responding to: ???'s previous message |
Newtons method for finding the square root of a positive number can be summerised as simply calculating the iterative formula
x(n)=1/2(x(n-1)+b/x(n-1)) just keep pluging the new value of x(n) into the formula until it converges. so to find the square root of 45 by calculator we know the square root of 45 is 6.7082 we make an initial quess lets say 4 x(1) then becomes 7.625 plugging 7.625 into the equation we get x(2)=6.7633 x(3)=6.7084 x(4)=6.7082 the easiest way to know when the answer has converged is when the difference between sucessive values is less than some value. the question of how long newtons method takes to converge for a given value leads to chaos theory. |
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