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Numerical algorithms are described for solving the eigenvalue assignment (EVA) problem for multi-input systems by means of state feedback. The multi-input EVA problem is first reduced to one or more single-input EVA problems where the single-input systems are in "upper Hessenberg form." An algorithm based on the well-known implicitly shifted QR algorithm is then described for solving the single-input EVA problem. Some variations on the use of these algorithms are also proposed to handle certain special cases. Numerical properties of the algorithms are discussed and examples are given to illustrate their numerical performance.