First differences of most negative eigenvalues of a symmetric matrix.

Mathematica 8:
Clear[a, t, n, k, i, j]
t[n_, 1] = 1;
t[1, k_] = 1;
t[n_, k_] :=
t[n, k] =
If[n >= k, -Sum[t[n - i, k], {i, 1, k - 1}], -Sum[
t[k - i, n], {i, 1, n - 1}]];
nn = 64;
a = Range[1, nn]*0;
b = Range[1, nn]*0;
Do[
m = Table[Table[t[n, k], {k, 1, j}], {n, 1, j}];
a[[j]] = Eigenvalues[m],
{j, 1, nn}]

Round[Table[-Min[N[a[[i]]]], {i, 1, nn}], 0.00001]
(*ListLinePlot[-Table[Min[N[a[[i]]]],{i,1,nn}]]*)
ListLinePlot[
Flatten[{0, -Differences[Table[Min[N[a[[i]]]], {i, 1, nn}]]}],
Ticks -> {Range[nn]}]
ListLinePlot[
Flatten[{0, Differences[Table[Max[Abs[N[a[[i]]]]], {i, 1, nn}]]}],
Ticks -> {Range[nn]}]

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One Response to First differences of most negative eigenvalues of a symmetric matrix.

  1. Wonderful website, thanks a lot !!

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