In this particular cases rational numbers provide an escape: hilbert 10x 1 1r2 1r3 1r4 1r5 1r6 1r7 1r8 1r9 1r10 1r2 1r3 1r4 1r5 1r6 1r7 1r8 1r9 1r10 1r11 1r3 1r4 1r5 1r6 1r7 1r8 1r9 1r10 1r11 1r12 1r4 1r5 1r6 1r7 1r8 1r9 1r10 1r11 1r12 1r13 1r5 1r6 1r7 1r8 1r9 1r10 1r11 1r12 1r13 1r14 1r6 1r7 1r8 1r9 1r10 1r11 1r12 1r13 1r14 1r15 1r7 1r8 1r9 1r10 1r11 1r12 1r13 1r14 1r15 1r16 1r8 1r9 1r10 1r11 1r12 1r13 1r14 1r15 1r16 1r17 1r9 1r10 1r11 1r12 1r13 1r14 1r15 1r16 1r17 1r18 1r10 1r11 1r12 1r13 1r14 1r15 1r16 1r17 1r18 1r19
x=: hilbert 10x y=: %. x >./|, (=i.10) - x +/ .* y 0 That is, y is the exact inverse. My favorite factoid on Hilbert matrices: H=: hilbert NB. synonym det=: -/ .* NB. determinant det H 5x 1r266716800000 % det H 5x NB. reciprocal is integral 266716800000 q: % det H 5x NB. prime factors 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 5 5 5 5 5 7 7 7 ~. q: % det H 5x NB. unique prime factors 2 3 5 7 i.&.(p:^:_1)@+: 5x NB. all primes < 2*n 2 3 5 7 (i.&.(p:^:_1)@+: -: [EMAIL PROTECTED]:@(%"_)@[EMAIL PROTECTED]) 5x 1 (i.&.(p:^:_1)@+: -: [EMAIL PROTECTED]:@(%"_)@[EMAIL PROTECTED]) 50x 1 ----- Original Message ----- From: John Randall <[EMAIL PROTECTED]> Date: Monday, January 15, 2007 9:25 am Subject: Re: [Jgeneral] Invert max and LAPACK > Joey K Tuttle wrote: > > On my G5 iMac - > > > > x=: 1000 1000 [EMAIL PROTECTED] 0 NB. random real matrix > > 6!:2 'y=: %. x' NB. invert it > > 13.7781 > > > > >./|, (=i.1000) - x +/ .* y NB. how accurate? > > 1.97126e_13 > > > > Random matrices tend to be numerically stable. Unstable ones crop > up all > the time. > > hilbert=:]\ %@(i.&.<:@+:) > x=:hilbert 10 > y=:%.x > >./|, (=i.10) - x +/ .* y > 0.108042 ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
