Gauss Newton algorithm

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	Gauss-Newton algorithm - Wikipedia, the free encyclopedia
		In mathematics, the Gauss-Newton algorithm is used to solve nonlinear least squares problems.
		We can conclude that the Gauss-Newton method is the same as Newton's method with the Σ f ∇²f term ignored.
		It is a modification of Newton's method that does not use second derivatives.
	en.wikipedia.org /wiki/Gauss-Newton_algorithm (198 words)

	publ.html
		The algorithm may be modified to be used in the presence of ideal diodes and is related to penalty and multiplier methods for constrained minimization and Davidenko's method for solving certain ill-conditioned systems of nonlinear equations.
		An algorithm is given for the efficient construction of ellipsoidal approximations to the sets involved and it is shown that this algorithm leads to linear control laws.
		We have developed distributed iterative algorithms for solving a more general version of this integer programming problem, which is of independent interest, and have shown that they find the optimal solution in a finite number of iterations which is polynomial in the number of power levels and the number of mobiles.
	web.mit.edu /dimitrib/www/publ.html (14378 words)

	Gauss-Newton Method
		An algorithm that is particularly suited to the small-residual case is the Gauss-Newton algorithm, in which the Hessian is approximated by its first term.
		The Gauss-Newton algorithm is used, usually with enhancements, in much of the software for nonlinear least squares.
		It is a component of the algorithms used by DFNLP, MATLAB, NAG(FORTRAN), NAG(C), OPTIMA, and TENSOLVE.
	www-fp.mcs.anl.gov /otc/Guide/OptWeb/continuous/unconstrained/nonlinearls/section2_1_1.html (314 words)

	JPT (Apr 2003): Experiences With Automated History Matching
		Critical input to the inverse Gauss-Newton algorithm is the sensitivity-coefficient matrix.
		The mathematical basis for the history-match algorithm and the computation of the sensitivity coefficients in this method are similar to those of Method 1.
		Most published AHM algorithms are impractical for large reservoir simulation models because they require excessive computational time.
	www.spe.org /spe/jpt/jsp/jptpapersynopsis/0,2439,1104_11040_1042282_1043252,00.html (1309 words)

	Neural Computing Research Group: Forthcoming Seminars
		An efficient distributed algorithm is devised on the basis of insight gained from the analysis and is examined using numerical simulations, showing excellent performance and full agreement with the theoretical results.
		From a practical point of view, the CGS algorithm is a better candidate for parallel implementation than the MGS variant of the same algorithm and this aspect could not be overlooked in certain computing environments.
		The least squares algorithm is initially applied to estimate the parameters in the autoregressive (AR) part of the linear subsystem.
	www.ncrg.aston.ac.uk /Seminars/forthcoming.html (2299 words)

	APP-CONF-List2-Abstract.asp?PaperNo=206
		A damage detection algorithm is presented based on updating a finite element model with measured eigenfrequencies and mode shapes.
		The algorithm is applied to a truss model with actual measured dynamic properties.
		Results show that the algorithm is capable of detecting location and extend of the simulated damage.
	www.sem.org /APP-CONF-List2-Abstract.asp?PaperNo=206 (175 words)

	history.txt
		The stacked Newton algorithm now uses less storage and is consequently faster with medium to large size models.
		The new algorithm is the same as that used by the Gauss package: A.J. Kinderman and J.G. Ramage, (1976), JASA, Vol 71, pp.
		The algorithm for generating normal pseudo-random numbers has been changed to improve the properties of generated random numbers.
	www.econ.surrey.ac.uk /winsolve/software/history.txt (1350 words)

	iTOUGH2 Minimization Algorithms
		The Levenberg-Marquardt modification of the Gauss-Newton algorithm for the minimization of non-quadratic objective functions was found to be an efficient and robust method for most iTOUGH2 inversions.
		After local linearization of the objective function with respect to the parameters to be estimated, the Levenberg-Marquardt algorithm performs initially small, but robust steps along the steepest descent direction, and switches to more efficient quadratic Gauss-Newton steps as the minimum is approached.
		The purpose of the minimization algorithm is to detect the minimum of the objective function in the n-dimensional parameter space.
	www-esd.lbl.gov /ITOUGH2/Minimization/minalg.html (514 words)

	IngentaConnect The Incremental Gauss-Newton Algorithm with Adaptive Stepsize Rul...
		IngentaConnect The Incremental Gauss-Newton Algorithm with Adaptive Stepsize Rul...
		In the paper, we propose a stepsize rule for EKF and establish global convergence of the algorithm under the boundedness of the generated sequence and appropriate assumptions on the objective function.
		A notable feature of the stepsize rule is that the stepsize is kept greater than or equal to 1 at each iteration, and increases at a linear rate of k under an additional condition.
	www.ingentaconnect.com /content/klu/coap/2003/00000026/00000002/05143949 (267 words)

	lsqcurvefit (Optimization Toolbox)
		This algorithm is a subspace trust region method and is based on the interior-reflective Newton method described in [1], [2].
		The algorithms used are described fully in the Standard Algorithms chapter.
		Since the large-scale algorithm does not handle under-determined systems and the medium-scale does not handle bound constraints, problems with both these characteristics cannot be solved by
	www.math.psu.edu /local_doc/matlab/toolbox/optim/lsqcurvefit.html (1337 words)

	The Joys of Using SLIM
		An interesting note about this is that, contrary to some rumors 10 subdivisions of 20-point Gauss quadrature (200 point evaluation) is not as accurate as 96-point Gauss quadrature with less than half the function evaluations.
		Gauss quadrature is so far superior in accuracy to any other method (e.g.
		Of course there are certain (unknown before the fact) cases where other methods are much faster; but I would rather spend less time experimenting with zillions of algorithms and let the machine sweat a little more.
	www25.brinkster.com /ranmath/numal/slim.htm (854 words)

	Vikas Raykar's Course Projects
		Gauss Newton method was the best in terms of localization eroor and the number of iterations required.
		A Constrained least mean square algorithm (also known as Frost Beamformer) was derived which is capable of iteratively adapting the weights of the sensor array to minimize noise power at the array output while maintaining a chosen frequency response in the look direction.
		First the Isomap and the LLE algorithm are discussed in detail.
	www.umiacs.umd.edu /users/vikas/projects/projects_grad.html (886 words)

	nls
		When the '"plinear"' algorithm is used, the conditional estimates of the linear parameters are printed after the nonlinear parameters.
		algorithm: character string specifying the algorithm to use.
		The other alternative is "plinear", the Golub-Pereyra algorithm for partially linear least-squares models.
	www.stat.umn.edu /R/library/stats/help/nls (415 words)

	DAKOTA: Method Commands
		The algorithm employs linear approximations to the objective and constraint functions, the approximations being formed by linear interpolation at N+1 points in the space of the variables.
		Output verbosity is observed within the Iterator (algorithm verbosity), Model (synchronize/fd_gradients verbosity), Interface (map/synch verbosity), Approximation (global data fit coefficient reporting),and AnalysisCode (file operation reporting) class hierarchies; however, not all of these software components observe the full granularity of verbosity settings.
		The DIRECT optimization algorithm is a derivative free global optimization method that balances local search in promising regions of the design space with global search in unexplored regions.
	endo.sandia.gov /DAKOTA/licensing/release/html-ref/MethodCommands.html (11331 words)

	International Journal of Mathematics and Mathematical Sciences
		The algorithm uses the projected Gauss-Newton Hessian in conjunction with an active set strategy that identifies active inequalities and a trust-region globalization strategy that ensures convergence from any starting point.
		We propose a new projected Hessian Gauss-Newton algorithm for solving general nonlinear systems of equalities and inequalities.
		We also present a global convergence theory for the proposed algorithm.
	www.univie.ac.at /EMIS/journals/IJMMS/volume-25/S0161171201002290.html (120 words)

	gauss.sha
		************************************************************************** * Estimation of a CES production function by the Gauss-Newton algorithm * Section 12.2.3b of Judge, Hill et al.
		GEN1 B1=0.5 GEN1 B2=0.5 GEN1 B3=-1 GEN1 B4=-1 * Maximum number of iterations NITER: 50 * Convergence criteria - the algorithm stops when the * gradient sum of squares is less than the value specified.
	shazam.econ.ubc.ca /examples/gauss.sha (55 words)

	The Four-dimensional Hopf Model
		The one instance in Table 4 where the Gauss-Newton algorithm clearly outperforms GENOUD presents the most interesting case for exploring the choice that can arise between locally efficient optimization, which is best performed by the BFGS, and effective global search by means of the EA part of GENOUD.
		The Gauss-Newton algorithm is run using analytical gradients while GENOUD is run using the built-in numerical gradients.
		We compare results from Gauss-Newton estimation using PROC MODEL to results from four configurations of GENOUD.
	jsekhon.fas.harvard.edu /genoud/node4.shtml (1172 words)

	Computer Science Colloquium Series - Fall 1999
		A least-squares formulation of this localization problem can then be solved by the Gauss-Newton algorithm.
		The running time of the algorithms is polynomial in the size of arithmetic circuit representing the input polynomial and the error parameter.
		Our algorithms first transform the input polynomial to a univariate polynomial and then use Chinese remaindering over univariate polynomials to efficiently test if it is zero.
	www.cs.iastate.edu /~colloq/colloquium-fall99.html (3977 words)

	2000 Consortium Report Abstracts
		This owes largely to the fact that the conjugate gradients-based algorithms avoid two computationally intensive tasks that are performed at each step of a Gauss-Newton iteration: calculation of the full Jacobian matrix of the forward modeling operator, and complete solution of a linear system on the model space.
		Numerical experiments involving synthetic and field data indicate that the two algorithms based on conjugate gradients (NLCG and Mackie-Madden) are more efficient than the Gauss-Newton algorithm in terms of both computer memory requirements and CPU time needed to find accurate solutions to problems of realistic size.
		The algorithm employs a nonlinear conjugate gradients (NLCG) scheme to minimize an objective function that penalizes data residuals and second spatial derivatives of resistivity.
	www-eaps.mit.edu /erl/research/report1/report2000.html (4149 words)

	Training Feedforward and Radial Basis Function Networks
		The Gauss-Newton method is a fast and reliable algorithm that may be used for a large variety of minimization problems.
		However, this algorithm may not be a good choice for neural network problems if the Hessian is ill-conditioned; that is, if its eigenvalues span a large numerical range.
		In general, however, the recommendation is to use one of the other, better, training algorithms and repeat the training a couple of times from different initial parameter initializations.
	documents.wolfram.com /applications/neuralnetworks/NeuralNetworkTheory/2.5.3.html (978 words)

	Stat 505: Week 4 Assignment (19-Feb-1998)
		The following link shows an example of an iterative fitting function that uses a Gauss-Newton algorithm.
		Implement a function that uses a Newton-Raphson iterative algorithm to fit the parameters alpha and beta, from which the ld50 is estimated.
		The function should take as input vectors d, n, and r, starting values for alpha and beta, and a limit for the number of iterations.
	www.biostat.umn.edu /~melanie/Spatial/Week7Assignment.html (602 words)

	Main Frame in Main Page
		Gauss statements can be included within the command file.
		Gaussx has full support for all Gauss PQG routines, while for GAUSSPlot, interactive customization of a graph can be saved and used in subsequent sessions.
		All Gauss commands, logical goto, DO loops, and Gauss procs can be used within a Gaussx file.
	www.econotron.com /gaussx/frmain.htm (1638 words)

	Examples of Different Training Algorithms
		When you use the backpropagation algorithm you have to choose the step size and the momentum.
		If you want examples of different training algorithms of more realistic sizes, see the ones in Chapter 8, Dynamic Neural Networks, or Chapter 12, Application Examples, and change the option
		This section includes a small example illustrating the different training algorithms used by
	documents.wolfram.com /applications/neuralnetworks/TrainingFeedforwardAndRadialBasisFunctionNetworks/7.2.0.html (572 words)

	Levenberg-Marquardt Method
		The ODRPACK algorithms use a trust-region Levenberg-Marquardt method that exploits the structure of this problem, so that there is little difference between the cost per iteration for this problem and the standard least squares problem in which the
		The algorithms in ODRPACK solve unconstrained nonlinear least squares problems and orthogonal distance regression problems, including those with implicit models and multiresponse data.
		The Levenberg-Marquardt algorithm has proved to be an effective and popular way to solve nonlinear least squares problems.
	www-fp.mcs.anl.gov /otc/Guide/OptWeb/continuous/unconstrained/nonlinearls/section2_1_2.html (276 words)

	armax (System Identification Toolbox)
		A robustified quadratic prediction error criterion is minimized using an iterative Gauss-Newton algorithm.
		The Gauss-Newton vector is bisected up to 10 times until a lower value of the criterion is found.
		, are constructed in a special four-stage LS-IV algorithm.
	www.tau.ac.il /cc/pages/docs/matlab/help/toolbox/ident/armax.html (331 words)

	Newton algorithm
		The Adjoint Newton Algorithm for Large-Scale Unconstrained Optimization in Meteo...
		Damped Newton Algorithms for Matrix Factorization with Missing Data...
		An active set Newton's algorithm for large-scale nonlinear programs with box con...
	www.scienceoxygen.com /signal/38.html (336 words)

	Cn-Cz
		The algorithm inductively learns a set of propositional if-then rules from a set of training examples by performing a general-to-specific beam search through rule-space for the best rule, removing training examples covered by that rule, and then repeating the process until no more good rules can be found.
		In the next step an initial network is constructed using an iterative algorithm that attempts to identify the smallest or least costly set of selection units that meet the objectives.
		The heart of the Coq system is a type-checking algorithm that checks the correctness of proofs.
	stommel.tamu.edu /~baum/linuxlist/linuxlist/node12.html (11570 words)

	Smirnova
		A principal point in the numerical implementation of regularized Newton's and Gauss-Newton's procedures is the computation of the operators (F'(x)+\alpha I)^{-1} and (F^{\prime*}(x)F'(x)+\alpha I)^{-1} respectively.
		In order to deal with it, a novel iteratively regularized algorithm with simultaneous updates of the operator (F^{\prime}(x_n)F'(x_n)+\alpha_n I)^{-1} is proposed: x_{n+1}=x_n-B_n [F^{\prime}(x_n)F(x_n)+\alpha_n(x_n-x_0)], B_{n+1}=[I-\lambda (F^{\prime*}(x_n)F'(x_n)+\alpha_n I)]B_n+\lambda I, A convergence theorem is proved.
		The stability of the process towards noise in the data is analyzed, and a stopping time is chosen so that the method converges as the noise level tends to zero.
	www-math.cudenver.edu /IMACS03/abs/smirnova.html (242 words)

	Optimization Toolbox 2.2 Release Notes (Optimization Toolbox Release Notes)
		The trust-region dogleg algorithm is now the default for medium-scale systems of equations where the number of equations is equal to the number of variables.
		It is based on the algorithm described in [1].
		function, which is used to solve systems of nonlinear equations, has a new default algorithm for medium-scale systems where the number of equations is equal to the number of variables.
	math.usask.ca /it/document/matlab6p5/base/relnotes/optim/optim13.html (261 words)

	Autoregressive Error Model
		The ULS and ML estimates employ a Gauss-Newton algorithm to minimize the sum of squares and maximize the log likelihood, respectively.
		The Gauss-Newton algorithm requires the derivatives of e or
		The Kalman filter algorithm, as it applies here, is described in Harvey and Phillips (1979) and Jones (1980).
	www.asu.edu /it/fyi/dst/helpdocs/statistics/sas/sasdoc/sashtml/ets/chap8/sect20.htm (1426 words)

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