Members of the Forum - If I'm approximating, e.g. the square root of 3, with a matrix method which returns an extended precision numerator and denominator, when I work out the decimal equivalent of this, at what point do I run out of significant digits?
For example, (1 3,:1 1)&(+/ .*)^:(5+i.5)],.1 0 NB. Successive approximations of %:3 76 44 208 120 568 328 1552 896 4240 2448 (%:3)-%/(1 3,:1 1)&(+/ .*)^:10],.x: 1 0 NB. How far off are successive approximations? _6.6086991e_6 (%:3)-%/(1 3,:1 1)&(+/ .*)^:20],.x: 1 0 _1.2607915e_11 (%:3)-%/(1 3,:1 1)&(+/ .*)^:30],.x: 1 0 _2.220446e_16 (%:3)-%/(1 3,:1 1)&(+/ .*)^:40],.x: 1 0 NB. More than 16 digits 0 (1 3,:1 1)&(+/ .*)^:40],.x: 1 0 NB. How precise is this in decimal? 144052522725670912 83168762773110784 2^.(1 3,:1 1)&(+/ .*)^:40],.x: 1 0 NB. Bits/number - relevant? 56.999373 56.206891 >From the progression of exponents in the cases for 10, 20, and 30 iterations, I'm guessing the answer should be about 21 significant digits but is there a way to better quantify this? Thanks, Devon -- Devon McCormick, CFA ^me^ at acm. org is my preferred e-mail ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
