Algorithm for Constructing the Chebyshev-Type Polynomials and the Chebyshev-Type Approximations with a Given Weight

The polynomials which give the minimum for the minimax norm are very useful in practical applications of various numerical algorithms. However, except the well-known Chebyshev's polynomials of first and second order there are no such polynomials specified in an explicit algebraic form. The paper considers the numerical algorithm(s) to generate the coefficients of the polynomials which: a) produce an optimal approximation for a given function in a minimax norm with some weight, b) produce an optimal deviation from zero with some weight and with a fixed high order coefficient.