Practical Comparison of Iterative Matrix Orthogonalization Algorithms

In previous work several algorithms for orthogonalizing the direction cosine matrix were introduced and their convergence rate and range were theoretically investigated. Three of the most promising algorithms are examined in this paper. lt is shown that the so-called Dual Algorithm is by far superior to the other two from the point of view of speed, computer memory, accuracy, and convergence rate. lt is therefore recommended that whenever the direction cosine matrix is computed by simple numerical integration of a matrix differential equation, the Dual Algorithm be used to orthogonalize the resultant matrix.