 For a near-orthogonal matrix, rapid convergence to the orthogonal factor can be achieved by a "Newton's method" approach due to (1990), repeatedly averaging the matrix with its inverse transpose.has published an accelerated method with a convenient convergence test.For example, consider a non-orthogonal matrix for which the simple averaging algorithm takes seven steps

and which acceleration trims to two steps (with = 0.353553, 0.565685).