Non-singular (n×n) matrices can be inverted by first factorizing them into matrices with lower condition numbers. Estimates are obtained which guarantee the accuracy of the computed inverse by the residual criterion and are identical as to the dependence on n of the accuracy of matrix multiplication. The inversion algorithm proposed here for symmetric positive-definite matrices, unlike Gholesky’s algorithm, does not break down entirely owing to the need to extract the root of a negative number and guarantees a positive-definite result.
