A procedure for inverting large symmetric matrices

In the least squares method for simultaneous adjustment of several parameters, the coefficients of the normal equations are the elements of a symmetric positive-definite matrix. In order to solve the normal equations and evaluate the precision measures of the resulting parameters, inversion of this matrix of coefficients is required. Many available procedures for matrix inversion do not take advantage of the symmetry. Thus, when programmed for a high-speed computer, all n2 elements must be stored and manipulated, whereas only n(n + 1)/2 of them are independent. In order to allow a computer of given memory capacity to handle a large matrix, the following procedure for inverting a symmetric matrix has been devised.1

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