Calculation of geodetic height on rectangular spatial coordinates of points of the terrestrial surface

In article relevance of a problem of independent calculation of geodetic height of N of spatial rectangular coordinates of X, Y, Z is noted. Merits and demerits of the used formulas for calculation of height are specified. A conclusion of high-precision algorithm for direct calculation of geodetic height of points of a terrestrial surface is given. The analysis on the precision of this algorithm by research on an extremum of the received expressions for an assessment of errors is made. For preliminary calculation of accuracy of height and the choice of computer facilities are expressed through initial data.