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An interior-point gradient method for large-scale totally nonnegative least squares problems

Thu, 08/27/2009 - 08:07 pm

Igor code for solving NNLS problems, coded using: http://www.caam.rice.edu/~zhang/reports/tr0408.ps (Michael Merritt and Yin Zhang, Technical Report TR04-08, Department of Computational and Applied Mathematics, Rice University, Houston, Texas 77005, U.S.A., May, 2004)
Abstract: We study an interior-point gradient method for solving a class of so-called totally nonnegative least squares problems. At each iteration, the method decreases the residual norm along a diagonally scaled negative gradient direction with a special scaling. We establish the global convergence of the method, and present some numerical examples to compare the proposed method with a few similar methods including the aﬃne scaling method.
This code is extracted from "Irena" package for modeling of small-angle scattering,where it is used for solving size distribution problem in small-angle scattering. Similar method is Maximum Entropy, regularization, etc.
Note: as coded can handle ONLY 1D data. The input data are in form of MeasuredData (as three waves: one with X values, one with Y values, and one with Uncertainties), and Model which is being desired (as two waves: one with X values and one with Y values). The code returns Y values for the Model. Please, read the reference for more details.

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