Quadratically optimized polynomials for fermion simulations

Quadratically optimized polynomials are described which are useful in multi-bosonic algorithms for Monte Carlo simulations of quantum field theories with fermions. Algorithms for the computation of the coefficients and roots of these polynomials are described and their implementation in the algebraic manipulation language Maple is discussed. Tests of the evaluation of polynomials on dynamical fermion configurations are performed. In a simple special case the obtained polynomial approximations are compared to Chebyshev polynomials.