Inverse of a Symmetric Partitioned Matrix

So for updating the Toeplitz matrix we can write,

(((({{Γ, g}, {(g^′), v}})))^(-1))=(({{(Γ^(-1))(
                  I + (Γ^(-1))/a), -h}, {(h^′), b}}))

<< LinearAlgebra`MatrixManipulation`

<< FGN.m

r = Table[FGNAcf[k, 0.7], {k, 0, 10}];

r5 = Take[r, 5];

R5 = toe[r5];

R5Inv = Inverse[R5];

GI = R5Inv; G = R5;

G2 = toe[Take[r, 6]];

MatrixForm[G2]

g = {r5, r[[6]]} // Flatten // Reverse // 
          Most;
v = G[[1, 1]];
e = 1/(v - g . GI . g); 
a = g . g*e;

MatrixForm[A = GI + (GI . Outer[Times, g, g] . GI)*e]

MatrixForm[Inverse[toe[Take[r, 6]]]]

e

f = -GI . g*e

(H = BlockMatrix[{{A, Partition[f, 1]}, {{f}, {{e}}}}]) // 
      MatrixForm