A Priori Prediction of Roundoff Error Accumulation in the Solution of a Super-Large Geodetic Norlam Equation System

摘要

The theory of roundoff errors for linear equations is adapted and applied to a linear system of 350,000 unknows, representing the normal equations of the U.S.-ground control network now being readjusted. The system is positive definite and sparse. Cholesky's algorithm is used. The equations are reordered in a way dictated by the Helmert blocking technique. The block design is based on nested dissection. A linear stochastic roundoff error progagation model is used. Two families of computers are considered that come close to representing the two extremal cases of true chopping and true rounding, the CDC 6600 (with the rounding option set into effect) and the IBM 360. Structural properties of the U.S. network relevant to roundoff error propagation are thoroughly investigated. Next to the large size of the network, weight singularities from observations of extremely high accuracy cause some concern. Bounds on bias and standard deviation of the individual components of the solution vector are derived. They indicate that the new adjustment of the North American Datum (NAD) is feasible on both types of computers.