QR decomposition
upper Hessenberg form first (for symmetric matrix this will be tridiagonal form). Which costs formula_50 arithmetic operations using a technique based on Householder reduction), with a finite sequence of orthogonal similarity transforms, somewhat like a two-sided QR decomposition. (For QR decomposition, the Householder rotations are multiplied only on the left, but for the Hessenberg case they are multiplied on both left and right.) For symmetric matrices this procedure costs formula_51 arithmetic operations using a technique based on Householder reduction.