Quote:
Originally Posted by Don Blazys
For instance, using the best and fastest computer available to you... to how many decimal places can you or any of the "math denizens" here at Hypography calculate the root of:
sin(x^(1/2))-ln(ln(x))= 6.2207156287787... ?
As you can see, the best that I can do with my TI-89 is only 13 decimal places, and I can't even be sure that the last several digits are correct!
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Well, despite your misleading equality, I supposed and verified that you mean finding a zero of the expression:
which can be done by methods such as those of Newton or Gauss; in some cases even regula falsi or the secant method may suffice. The standard computational type double has a 53 bit mantissa, it can improve precision somewhat compared with your result. If you really find it important to improve precision on that computation you could always contruct an ad hoc numeric type or use a language which handles higher precision, perhaps Craig's favourite language would suit the purpose.
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Inutil insegnŕ al mus, si piart timp, in plui si infastiděs la bestie.
Hypography Forum PITA...... er, Administrator.
