Laguerre-like inclusion method for polynomial zeros

A new method of the fourth order for the simultaneous inclusion of simple polynomial zeros is proposed. The presented method is based on the fixed point relation of Laguerreʹs type and realized in circular complex interval arithmetic. The established initial conditions guarantee the convergence of the considered method and the fourth order of convergence. These conditions are computationally verifiable, which is of practical importance. The presented iteration formula is suitable for the construction of modified interval methods with improved convergence rate with negligible additional operations. Convergence analysis and numerical results are given.