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The QR algorithm computes eigenvalues through repeated QR decompositions and similarity updates. Shifted and unshifted forms have different convergence rates; the unshifted QR algorithm uses a zero shift at every step.

The unshifted QR algorithm factors $A_k=Q_k{R}_k$ and forms $A_{k+1}=R_k{Q}_k=Q_k^T{A}_k{Q}_k$, preserving eigenvalues while driving the matrix toward block diagonal form.

This is the zero-shift case of the QR algorithm.