A program for total (orthogonal) least squares in compact storage mode

Total (orthogonal) least squares considers the least‐squares problem when data errors occur in both the vector of the right‐hand side and in the matrix of the equations of condition. A total least‐squares solution may be calculated by use of the singular value decomposition (SVD), but this is computationally much more demanding than use of the normal equations and requires more memory, particularly when there are many more equations than unknowns. A FORTRAN program is given to calculate a total least‐squares solution from normal equations stored in compact mode; only the upper triangular part of the matrix is stored. If the total least‐squares solution does not exist, the program calculates an ordinary least‐squares solution. Two examples illustrating use of the program are presented.