Numerical algorithms for solving nonlinear L р-norm estimation problems: part II - a mixture method for large residual and illo-conditioned problems |
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| Authors: | R Gonin SHC du Toit |
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| Institution: | 1. Institute of Biostatitics , Medical Research Council , Cape Town;2. Institute of Statistical Research , Human Scienes Research Council , Pretoria |
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| Abstract: | The nonlinear least squares algorithm of Gill and Murray (1978) is extended and modified to solve nonlinear L р-norm estimation problems efficiently. The new algorithm uses a mixture of 1st-order derivative (Guass-Newton) and 2nd-order derivative (Newton) search directions. A new rule for selecting the “grade” r of the p-jacobiab matrix Jp was also incorporated. This brought about rapid convergence of the algorithm on previously reported test examples. |
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| Keywords: | Nonlinear models L p-norm parameter estimation Guass-Newton large residual problems least squares singular-value decomposition modified Choleski decomposition |
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