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Data Fitting Problems With Bounded Uncertainties In The Data
 SIAM J. MATRIX ANAL. APPL
, 2001
"... An analysis of a class of data tting problems, where the data uncertainties are subject to known bounds, is given in a very general setting. It is shown how such problems can be posed in a computationally convenient form, and the connection with other more conventional data fitting problems is exami ..."
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Cited by 8 (2 self)
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An analysis of a class of data tting problems, where the data uncertainties are subject to known bounds, is given in a very general setting. It is shown how such problems can be posed in a computationally convenient form, and the connection with other more conventional data fitting problems is examined. The problems have attracted interest so far in the special case when the underlying norm is the least squares norm. Here the special structure can be exploited to computational advantage, and we include some observations which contribute to algorithmic development for this particular case. We also consider some variants of the main problems and show how these too can be posed in a form which facilitates their numerical solution.
Robust Solutions To Linear Approximation Problems Under Ellipsoidal Uncertainty
 TOTAL LEAST SQUARES AND ERRORSIN VARIABLES MODELING, KLUWER
, 2002
"... The problem of tting a linear model to data, under uncertainty which can be regarded as being ellipsoidal, is considered in a very general setting. For a range of such problems, robust counterparts are established, and methods of solution are considered. ..."
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Cited by 2 (1 self)
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The problem of tting a linear model to data, under uncertainty which can be regarded as being ellipsoidal, is considered in a very general setting. For a range of such problems, robust counterparts are established, and methods of solution are considered.
Models For Robust Estimation And Identification
, 2003
"... In this paper, estimation and identification theories will be examined with the goal of determining some new methods of adding robustness. The focus will be upon uncertain estimation problems, namely ones in which the uncertainty multiplies the quantities to be estimated. Mathematically the problem ..."
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Cited by 1 (1 self)
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In this paper, estimation and identification theories will be examined with the goal of determining some new methods of adding robustness. The focus will be upon uncertain estimation problems, namely ones in which the uncertainty multiplies the quantities to be estimated. Mathematically the problem can be stated as, for system matrices and data matrices that lie in the sets (A + #A) and (b + #b) respectively, find the value of x that minimizes the cost (b + #b)#. The proposed techniques are compared with currently used methods such as Least Squares (LS), Total Least Squares (TLS), and Tikhonov Regularization (TR). Several results are presented and some future directions are suggested.