The problem of slow convergence in sequential estimates of covalent la
ttice constants is overcome by employing a new linear convergence acce
lerator. Chebyshev polynomials have been exploited to generate this tr
ansformation. It is simple, sufficiently accelerative and expressible
in a closed form, thus providing enough computational convenience. Per
formance of the scheme with relation to a few others is tested. Demons
trative calculations highlighting its worth and efficiency involve the
rapid and accurate evaluation of a few cubic lattice constants.