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2 edition of Solving dense nonlinear least-squares problems on a multiprocessor found in the catalog.

Solving dense nonlinear least-squares problems on a multiprocessor

Thomas F. Coleman

Solving dense nonlinear least-squares problems on a multiprocessor

by Thomas F. Coleman

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Published by Cornell Theory Center, Cornell University in Ithaca, N.Y .
Written in English


Edition Notes

Other titlesSolving dense nonlinear least squares problems on a multiprocessor.
StatementThomas F. Coleman, Paul E. Plassmann.
SeriesTechnical report / Cornell Theory Center -- CTC90TR22., Technical report (Cornell Theory Center) -- 22.
ContributionsPlassmann, Paul E., Cornell Theory Center.
The Physical Object
Pagination27 p. :
Number of Pages27
ID Numbers
Open LibraryOL16956907M

Introductions and definitions. Descent methods. Nonlinear least squares problems. Appendix. Linear Fitting Problems. C.L. Lawson and R.J. Hanson (). Solving Least Squares Problems, Prentice-Hall, Englewood Cliffs, ted with a detailed ``new developments'' appendix in by SIAM Publications, Philadelphia, PA.

Step 3. Solve this system. Note that any solution of the normal equations (3) is a correct solution to our least squares problem. Most likely, A0A is nonsingular, so there is a unique solution. If A0A is singular, still any solution to (3) is a correct solution to our problem. In this case, there will be infinitely many.   Finding the line of best fit using the Nonlinear Least Squares method. Covers a general function, derivation through Taylor Series.

  solve_least_squares_lm This is a function for solving non-linear least squares problems. It uses the traditional Levenberg-Marquardt technique. It is appropriate for small residual problems (i.e. problems where the terms in the least squares . Approximately solve and refine a local model of () around x k. until an improved solution estimate x k+1 is found ; Check whether x k+1 is optimal; set k= k+ 1. end Algorithm 1: Framework for Nonlinear Optimization Methods In this paper, we review the basic components of methods for solving .


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Solving dense nonlinear least-squares problems on a multiprocessor by Thomas F. Coleman Download PDF EPUB FB2

Coleman T.F., Plassmann P.E. () Solution of nonlinear least squares problems on a multiprocessor. In: van Zee G.A., van de Vorst J.G.G. (eds) Parallel Computing Shell Cited by: 9. problems, the objective function f(x) is a sum of squares of nonlinear functions f(x) = 1 2 Xm j=1 (r j(x))2 = 1 2 jjr(x)jj2 2 that needs to be minimized.

We consider the following problem min x f(x) = Xm j=1 (r j(x))2: This is a nonlinear least squares unconstrained minimization problem. It is called least squares because we are minimizing the File Size: KB. () Sparse Stretching for Solving Sparse-Dense Linear Least-Squares Problems.

SIAM Journal on Scientific ComputingAA Abstract | PDF ( KB)Cited by: 2. Example 0 1 2 3 40 2 4 0 2 4 x1 x2 graphofkf¹xºk 0 1 2 3 4 0 1 2 3 4 x1 x 2 contourlinesofkf¹xºk2 correctpositionisxex = „1;1” fivepointsai.

the problem of motion stereo ie. jointly estimating the motion and scene geom-etry from pairs of images of a monocular sequence. We show that our learned optimizer is able to efficiently and effectively solve this challenging optimization problem.

Keywords: Optimization SLAM Least Squares Gauss-Newton Levenberg-Marquadt 1 IntroductionCited by: Optimization and Data Fitting { Nonlinear Least-Squares Problems 2 Non-linearity A parameter α of the function f appears nonlinearly if the derivative ∂f/∂α is a function of α.

The model M (x,t) is nonlinear if at least one of the parameters in x appear nonlinearly. For example, in. Nonlinear Least Squares Data Fitting D.1 Introduction A nonlinear least squares problem is an unconstrained minimization problem of the form minimize x f(x)= m i=1 f i(x)2, where the objective function is defined in terms of auxiliary functions {f i}.It is called “least squares” because we are minimizing the sum of squares of these functions.

A least squares problem is a special variant of the more general problem: Given a function F:IR n7!IR, find an argument of that gives the minimum value of this so-calledobjective function or cost function.

Definition Global Minimizer Given F: IR n 7!IR. Find x+ = argmin xfF()g: This problem is very hard to solve in general, and we only. The following subroutines are provided for solving nonlinear least-squares problems: NLPLM Levenberg-Marquardt Least-Squares Method NLPHQN Hybrid Quasi-Newton Least-Squares Methods A least-squares problem is a special form of minimization problem where the objec-tive function is defined as a sum of squares of other (nonlinear) functions.

f (x. Di culty of solving nonlinear least squares problem I solving nonlinear equations or nonlinear least squares problem is (in general) much harder than solving linear equations I even determining if a solution exists is hard I so we will use heuristic algorithms {not guaranteed to always work {but often work well in practice (like k-means.

Nonlinear least squares problems are extremely important in many domains of mathematical programming applications, e.g. maximum likelihood estimations, nonlinear data fitting or parameter.

Much is to be gained by adopted non-linear processes for problem solving and we can see evidence of this by looking at the non-linear problem solving model found in Six Sigma. Six Sigma uses a model that is comprised of the following key steps: practical problem à statistical problem à statistical solution à practical solution.

An algorithm for solving the general nonlinear least-square problem is developed. An estimate for the Hessian matrix is constructed as the sum of two matrices.

The first matrix is the usual first-order estimate used by the Gauss method, while the second matrix is generated recursively using a rank-one formula.

Test results indicate that the method is superior to the standard Gauss method and. Basic example of nonlinear least squares using the problem-based approach. Nonlinear Data-Fitting Using Several Problem-Based Approaches.

Solve a least-squares fitting problem using different solvers and different approaches to linear parameters. Fit ODE, Problem-Based. Fit parameters on an ODE using problem-based least squares.

The Levenberg-Marquardt algorithm [Levenberg] [Marquardt] is the most popular algorithm for solving non-linear least squares problems. It was also the first trust region algorithm to be developed [Levenberg] [Marquardt]. Large sparse least squares problems arise in many applications, including geodetic network adjustments and finite element structural analysis.

Although geodesists and engineers have been solving such problems for years, it is only relatively recently that numerical analysts have turned attention to them. Solving large sparse systems of nonlinear equations and nonlinear least squares problems using tensor methods on sequential and parallel computers for solving dense systems of nonlinear equations and nonlinear least squares problems on a distributed-memory MIMD multiprocessor.

Experimental results obtained on an Intel iPSC2 hypercube. This can be expensive for large problems, so it is usually better to determine the sparsity structure. MaxPCGIter: Maximum number of PCG (preconditioned conjugate gradient) iterations, a positive scalar.

The default is max(1,numberOfVariables/2). For more information, see Large Scale Nonlinear Least Squares. PrecondBandWidth. Björck [2] discusses algorithms for linear least-squares problems in a comprehensive survey that covers, in particular, sparse least-squares problems and nonlinear least-squares.

Bates, D. and Watts, D. Nonlinear Regression Analysis and Its Applications, John Wiley &, Inc., New York. Björck, A. Least squares methods. Using the nonlinear least-squares API, you are able to model a nonlinear least-squares problem in standard form above and use the Gauss-Newton Hessian option.

The Gauss-Newton Hessian provides a positive semi-definite Hessian approximation (where is the Jacobian matrix of the residual functions) at every iteration and has good local.

For the type of problems you show in your examples (fitting degradation data with several transformation products), I created the mkin package as a convenience wrapper to FME for this type of problem. So let's see how mkin performs in these cases.Publisher Summary. This chapter discusses modification methods.

Of the many algorithms in existence for solving a large variety of problems, most of the successful ones require the calculation of a sequence {x k} together with the associated sequences {f k} and {J k}, where J k is the Jacobian of f evaluated at x es of these are Newton's method for nonlinear equations, the Gauss.Non-linear least squares is the form of least squares analysis used to fit a set of m observations with a model that is non-linear in n unknown parameters (m ≥ n).It is used in some forms of nonlinear basis of the method is to approximate the model by a linear one and to refine the parameters by successive iterations.