Performing armchair roundoff analyses of statistical algorithms

References

• Beaton , A. , Rubin , D. and Barone , J. 1976 . The acceptability of regression solutions: another look at computational accuracy . J. Amer. Statist. Assoc. , 71 : 158 – 168 .
   Web of Science ®Google Scholar
• Frane , J. 1978 . Proc. Comp. Sci. Statist.: 11th Ann. Symp. on the Interface . Methods in BMDP for dealing with ill-conditioned data—multicollinearity and multivariate outliers . 1978 . pp. 209 – 214 .
   Google Scholar
• Gentleman , M. 1973 . Least squares computations by Givens transformations without square roots . J. Inst. Math. Appl. , 12 329 – 336 .
   Google Scholar
• Gentleman , M. 1974 . Regression problems and the QR decomposition . Bull. Inst. Math. Appl. , 10 195 – 197 .
   Google Scholar
• Gentleman , M. 1975 . Error analysis of QR decompositions by Givens transformations . Linear Algebra Appl. , 10 189 – 197 .
   Google Scholar
• Golub , G. , Klema , V. and Stewart , G. 1977 . “ Rank degeneracy and least squares problems ” . In Working Paper No. 165 , New York, N.Y : National Bureau of Economic Research .
   Google Scholar
• Hammarling , S. 1974 . A note on modifications to the Givens plane rotation . J. Inst. Math. Appl. , 13 : 215 – 218 .
   Google Scholar
• Hoaglin , D. and Welsch , R. 1978 . The hat matrix in regression and ANOVA . Amer. Statistician , 32 : 17 – 22 .
   Web of Science ®Google Scholar
• Larson , J. and Sameh , A. 1978 . Efficient calculation of the effects of roundoff errors . ACM Trans. Math. Software. , To appear in
   Google Scholar
• Lawson , C. and Hanson , R. 1974 . Solving Least Squares Problems , Englewood Cliffs, N. J : Prentice-Hall. .
   Google Scholar
• Linnainmaa , S. 1976 . Taylor expansion of the accumulated rounding error . BIT , 16 : l46 – 160 .
   Google Scholar
• Miller , W. 1975a . Software for roundoff analysis . ACM Trans. Math. Software , 2 : 108 – 128 .
   Google Scholar
• Miller , W. 1975b . Computer search for numerical instability . J. Assoc. Comput. Mach. , 22 : 512 – 521 .
   Google Scholar
• Miller , W. 1976 . Roundoff analysis by direct comparison of two algorithms . SIAM J. Numer. Anal. , 13 : 382 – 392 .
   Google Scholar
• Miller , W. and Spooner , D. 1978 . Software for roundoff analysis, II . ACM Trans. Math. Software. , To appear in
   Google Scholar
• Moler , C. 1972 . Matrix computations with Fortran and paging . Commun. Assoc. Comput. Mach. , 15 : 268 – 270 .
   Web of Science ®Google Scholar
• Ryan , T. , Joiner , B. and Ryan , B. 1976 . Minitab Student Handbook , North Scituate, Mass : Duxbury Press .
   Google Scholar
• Smith , B. , Boyle , J. , Garbow , B. , Ikebe , Y. , Klema , V. and Moler , C. 1974 . Matrix Eigensystem Routines—EISPACK Guide , New York : Springer-Verlag .
   Google Scholar
• Stewart , G. 1973 . Introduction to Matrix Computations , New York : Academic Press .
   Google Scholar
• Velleman, P., Seaman, J. & Allen, I. (1978). Evaluating accuracy and cost of computer programs for multiple regression: theory, methods, and an application to widely distributed statistical packages. Submitted for publication.
   Google Scholar
• Wampler , R. 1970 . On the accuracy of least squares programs . J. Amer. Statist. Assoc. , 65 : 549 – 565 .
   Web of Science ®Google Scholar