John E. Dennis
- 1 ALLEN, D M Private commumcatlon, 1976Google Scholar
- 2 BARD, Y Comparison of gradmnt methods for the solutmn of nonhnear parameter estimation problems SIAM J Numer Anal 7 (1970), 157-186Google Scholar
- 3 BARD, Y Nonltnear Parameter Esttmatmn Academic Press, New York, 1974Google Scholar
- 4 BATES, D M, AND WATTS, D G An orthogonahty convergence criterion for nonhnear least squares Queen's Mathematmal Preprmt 1979-14, Queen's Umv, Kingston, Ont., Canada, 1979Google Scholar
- 5 BEALE. E M L On an lteratlve method for finding a local mlmmum of a function of more than one va~mble Tech Rep 25, Statistical Tecbmques Research Group, Princeton Umv., Princeton, N J, 1958Google Scholar
- 6 BELSLEY, D A On the efficmnt computation of the nonhneal full-mformation maximum hkehhood estimator Tech Rep 5, Center for Computational Research in Economics and Management Science, Massachusetts institute of Technology, Cambridge, Mass, 1980Google Scholar
- 7 BETTS, J T Solving the nonhnear least squazes problem Apphcatlon of a general method J Optzm Theory Appl 18 (1976), 469-484Google Scholar
- 8 Box, M J A comparison of several current optimization methods and the use of transformations m constrained problems Comput J 9 (1966), 67-77Google Scholar
- 9 BRANIN, F H Widely convergent method for finding multiple solutions of simultaneous nonlinear equations IBM J Res Develop 16 (197I), 504-522Google Scholar
- 10 BROWN, K M, AND DENNIS, J.E A new algorithm for nonhnear least-squares curve fitting In Mathemattcal Software, J R Rice, Ed., Academm Press, New York, 1971, 391-396.Google Scholar
- 11 COLVILLE, A R A comparative study of nonhnear programming codes Tech Rep 320-2949, IBM New York Scientific Center, 1968Google Scholar
- 12 CRAG(~, E E, AND LEVY, A V Study on a supermemory gradient method for the minimization of functmns J Optzm Theory Appl 4 (1969), 191-205Google Scholar
- 13 DAVIDON, W C New least-square algorithms J Opttm Theory Appl 18 (I976), 187-i97.Google Scholar
- 14 DENNIS, J E Some computatmnal techniques for the nonhnear least squares problem In Numertcal Soluttons of Systems of Nonhnear Equations, G D Byrne and C A Hall, Eds, Academm Press, New York, 1973, pp t57-183Google Scholar
- 15 DENNIS, J E Nonlinear least squares and equatmns In The State of the Art tn Numertcal Analysts, D Jacobs, Ed, Academic Press, London, 1977, pp 269-312Google Scholar
- 16 DENNIS, J E, AND MEI, H.H-W Two new unconstrained optimization algorithms which use functmn and gradmnt values J Opttm Theory Appl 28 (1979), 453-482Google Scholar
- 17 DENNIS, J E, AND MORI~, J J Quasi-Newton methods, motivatmn and theory SIAM Rev 19 (1977), 46-89Google Scholar
- 18 DENNm, J.E, AND WF.LSCH, R E. Techmques for nonhnear least squares and robust regress|on. Commun Stattst B7 (I978), 345-359Google Scholar
- 19 ENGVALL. J L Numerical algomthm for solving over-determined systems of nonlinear equatmns NASA Document N70-35600, 1966Google Scholar
- 20 FLETCHER, 1:~ Function minimization without evaluating derlvatlves--A review Comput J 8 (1965), 33-41Google Scholar
- 21 FLETCI4F~R, R A modified Marquardt subroutine for nonhnear {east squares Rep R6799, AERE, Harwell, England, 1971Google Scholar
- 22 FLETCHER, R., AND POWELL, M.J D A rapidly convergent descent method for minimization. Comput J 6 (1963), 163-168Google Scholar
- 23 FREUDENSTEIN, F, AND ROTH, B Numerical solutmn of systems of nonlinear equations J, ACM 10, 4 (Oct 1963), 550-556 Google Scholar
- 24 GA'~, D M Computing optimal |ocaUy constrained steps SIAM J Sc~ StatLst. Comput 2, 2 (June 1981), 186-I97Google Scholar
- 25 GAY, D M Subroutines for general unconstrained mlmmlzatlon usmg the model/trust-region approach Tech Rep 18, Cemer for Computational Research m Economics and Management Scmnce, Massachusetts Institute of Technology. 1980Google Scholar
- 26 GILL, P E, AND MURRAY, W Algorithm for the solution of the nonlinear least-squares problem SIAM J Numer. Anal 15 (1978), 977-992Google Scholar
- 27 GOLUB, G H Matrix decompositions and staUstwal calculations In Statlsttcal Computatmn, R.C Milton and J.A. Nelder, Eds, Academic Press, New York, 1969, pp 365-397Google Scholar
- 28 JENNRmH, R I, AND SAMPSON, P F Apphcation of step-wise regression to nonlinear estimation. Technometmcs 10 (1968), 63-72Google Scholar
- 29 KOWALIK, J S, AND OSBORNE, M R Methods for Unconstrazned Opttmlzatton Problems, American Elsevier, New York, 1968Google Scholar
- 30 MEYER, R R Theoretical and computational aspects of nonlinear regression In Nonhnear Programmtng, J B Rosen, O L Mangasarlan, and K Rltter, Eds, Academm Press, New York, 1970Google Scholar
- 31 MORE, J J The Levenberg-Marquardt algorithm Implementation and theory In Lecture Notes zn Mathemattcs No 630 Numerical Analys,s, G Watson, Ed, Sprmger-Verlag, New York, 1978, pp 105-i16Google Scholar
- 32 MORR, J J. implementation and testing of optimization software DAMTP Rep 79/NA4, Cambridge Umv, Cambridge, England, 1979Google Scholar
- 33 OREN, S S Self-scaling variable metric algorithms without line search for unconstrained minimization Math Comput 27 {i973), 873-885.Google Scholar
- 34 OSBORNE, M R Some aspects of nonhnear least squares calculations In Numerwal Methods for Nonhnear Opttm,zatzon, F A Lootsma, Ed., Academic Press, New York, 1972Google Scholar
- 35 POWELL, M J D An iteratlve method for finding stationary values of a function of several variables Comput J 5 {1962), 147-151Google Scholar
- 36 POWELL, M J.D A FORTRAN subroutine for unconstrained mlmmization, requiring first derivatives of the objective function. Rep AERE-R.6469, AERE Harwell, England, 1970.Google Scholar
- 37 PRATT, J W When to stop a quasi-Newton search for a maximum hkehhood estimate Working Paper 77-16, Harvard School of Business, Cambridge, Mass., 1977Google Scholar
- 38 RAO, C R. L~near Statlsttcal Inference and Its Appltcatmns, 2nd ed, Wiley, New York, 1973.Google Scholar
- 39 REINSCH, C H. Smoothing by sphne functions. II Numer Math 16 (1971), 451-454Google Scholar
- 40 ROSENBROCK, H H An automatic method for finding the greatest or least value of a function Comput J 3 (1960), 175-184Google Scholar
- 41 WEDIN, P-A The non-hnear least squares problem from a numerical point of view, i and II Comput Sci Tech Reps, Lund Umv, Lund, Sweden, 1972 and 1974.Google Scholar
- 42 WEt)IN, P -A On surface dependent properties of methods for separable non-linear least squares problems ITM Arbetsrapport nr 23, Inst for Tellampad Matematlk, Stockholm, Sweden, 1974.Google Scholar
- 43 WEt)IN, P-A. On the Gauss-Newton method for the non-hnear least squares problem ITM Arbetsrapport nr 24, Inst for Tellampad Matematik, Stockholm, Sweden, 1974.Google Scholar
- 44 ZANGWILL, W J Nonhnear programming via penalty functmns Manage Sc~ 13 (1967), 344- 358Google Scholar
Index Terms
- An Adaptive Nonlinear Least-Squares Algorithm
Recommendations
Total least mean squares algorithm
Widrow (1971) proposed the least mean squares (LMS) algorithm, which has been extensively applied in adaptive signal processing and adaptive control. The LMS algorithm is based on the minimum mean squares error. On the basis of the total least mean ...
Algorithms for Constrained and Weighted Nonlinear Least Squares
A hybrid algorithm consisting of a Gauss--Newton method and a second-order method for solving constrained and weighted nonlinear least squares problems is developed, analyzed, and tested. One of the advantages of the algorithm is that arbitrarily large ...
Comments