A Report on the Accuracy of Some Widely Used Least Squares Computer Programs

Abstract Linear least squares test problems based on fifth degree polynomials have been run on more than twenty different computer programs in order to assess their numerical accuracy. The programs tested, all in present-day use, included representatives from several statistical packages as well as some from the SHARE library. Essentially five different algorithms were used in the various programs to obtain the coefficients of the least squares fits. The tests were run on several different computers, in double precision as well as single precision. By comparing the coefficients reported, it was found that those programs using orthogonal Householder transformations, classical Gram-Schmidt orthonormalization or modified Gram-Schmidt orthogonalization were generally much more accurate than those using elimination algorithms. Programs using orthogonal polynomials (suitable only for polynomial fits) also proved to be superior to those using elimination algorithms. The most successful programs accumulated inner...

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