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// The Great Computer Language Shootout↩
//↩
// contributed by Ian Osgood↩
↩
function A(i,j) {↩
return 1/((i+j)*(i+j+1)/2+i+1);↩
}↩
↩
function Au(u,v) {↩
for (var i=0; i<u.length; ++i) {↩
var t = 0;↩
for (var j=0; j<u.length; ++j)↩
t += A(i,j) * u[j];↩
v[i] = t;↩
}↩
}↩
↩
function Atu(u,v) {↩
for (var i=0; i<u.length; ++i) {↩
var t = 0;↩
for (var j=0; j<u.length; ++j)↩
t += A(j,i) * u[j];↩
v[i] = t;↩
}↩
}↩
↩
function AtAu(u,v,w) {↩
Au(u,w);↩
Atu(w,v);↩
}↩
↩
function spectralnorm(n) {↩
var i, u=[], v=[], w=[], vv=0, vBv=0;↩
for (i=0; i<n; ++i) {↩
u[i] = 1; v[i] = w[i] = 0;↩
}↩
for (i=0; i<10; ++i) {↩
AtAu(u,v,w);↩
AtAu(v,u,w);↩
}↩
for (i=0; i<n; ++i) {↩
vBv += u[i]*v[i];↩
vv += v[i]*v[i];↩
}↩
return Math.sqrt(vBv/vv);↩
}↩
↩
for (var i = 6; i <= 48; i *= 2) {↩
spectralnorm(i);↩
}↩