Symmetric row/column update of a size-n symmetric eigenvalue problem

The matrix to diagonalize is given in the form

A = D + e(p) u^T + u e(p)^T

where D is a diagonal matrix with diagonal elements {d_k, k=1,...,n}, u is a given column-vector, and the vector e(p) with components e(p)_i=δ_ip is a unit vector in the direction p where 1≤p≤n.

Given the diagonal elements of the matrix D, the vector u, and the integer p, calculate the eigenvalues of the matrix A using O(n²) operations (see section "Eigenvalues of updated matrix" in the book).