On approximation with nonorthogonal systems

A problem of the least square approximation for non-periodic function was discussed when some nonorthogonal systems were used (powers and so called double period). The main difficulty was how to solve an ill-possed linear equations system for coefficients of approximation. Round-off errors were investigated for explicite methods of Gauss and square root. Optimal orders of systems were found, and some recomendations were proposed for practical calculations. The double period method occurs very perspective and may be an alternative to the wavelet-analyses.