ODRPACK is a software package for weighted orthogonal distance regression, i.e., for finding the parameters that minimize the sum of the squared weighted orthogonal distances from a set of observations to the curve or surface determined by the parameters. It can also be used to solve the nonlinear ordinary least squares problem. The procedure has application to curve and surface fitting, and to measurement error models in statistics. ODRPACK can handle both explicit and implicit models, and will easily accommodate complex and other types of multiresponse data. The algorithm implemented is an efficient and stable trust region Levenberg-Marquardt procedure that exploits the structure of the problem so that the computational cost per iteration is equal to that for the same type of algorithm applied to the nonlinear ordinary least squares problem. The package allows a general weighting scheme, provides for finite difference derivatives, and contains extensive error checking and report generating facilities.

References in zbMATH (referenced in 20 articles )

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  1. Bergström, Per; Edlund, Ove; Söderkvist, Inge: Efficient computation of the Gauss-Newton direction when fitting NURBS using ODR (2012)
  2. Forbes, Alistair B.; Minh, Hoang D.: Form assessment in coordinate metrology (2011)
  3. Zhang, J.L.; Wang, Y.; Zhang, X.S.: Superlinearly convergent trust-region method without the assumption of positive-definite Hessian (2006)
  4. Aster, Richard C.; Borchers, Brian; Thurber, Clifford H.: Parameter estimation and inverse problems (2005)
  5. Ahn, Sung Joon: Least squares orthogonal distance fitting of curves and surfaces in space. (2004)
  6. Björck, Åke: QR factorization of the Jacobian in some structured nonlinear least squares problems (2002)
  7. Hermey, Damaris; Watson, G.Alistair: Fitting data with errors in all variables using the Huber M-estimator (1999)
  8. Nocedal, Jorge; Wright, Stephen J.: Numerical optimization (1999)
  9. Watson, G.A.: Choice of norms for data fitting and function approximation (1998)
  10. Strebel, Rolf; Sourlier, David; Gander, Walter: A comparison of orthogonal least squares fitting in coordinate metrology (1997)
  11. Watson, G.A.: Aspects of approximation with emphasis on the univariate case (1997)
  12. Bradley, Elizabeth; Stolle, Reinhard: Automatic construction of accurate models of physical systems (1996)
  13. Helfrich, H.-P.; Zwick, D.: A trust region algorithm for parametric curve and surface fitting (1996)
  14. Butler, B.P.; Cox, M.G.; Forbes, A.B.: The reconstruction of workpiece surfaces from probe coordinate data (1994)
  15. Gander, Walter; Golub, Gene H.; Strebel, Rolf: Least-squares fitting of circles and ellipses (1994)
  16. Marin, Samuel P.; Smith, Philip W.: Parametric approximation of data using ODR splines (1994)
  17. Helfrich, H.-P.; Zwick, D.: A trust region method for implicit orthogonal distance regression (1993)
  18. Schwetlick, Hubert: Nichtlineare Parameterschätzung: Modelle, Schätzkriterien und numerische Algorithmen (1991)
  19. Watson, G.A.; Yiu, K.F.C.: On the solution of the errors in variables problem using the $l\sb 1$ norm (1991)
  20. Boggs, Paul T.; Donaldson, Janet R.; Byrd, Richard H.; Schnabel, Robert B.: Algorithm 676: ODRPACK: Software for weighted orthogonal distance regression (1989)