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On the solution of equality constrained quadratic programming problems arising . . .
, 1998
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Recursive least squares with linear constraints
 in Proceedings of the 38th IEEE Conference on Decision and Control
, 1999
"... Abstract. Recursive Least Squares (RLS) algorithms have widespread applications in many areas, such as realtime signal processing, control and communications. This paper shows that the unique solutions to linearequality constrained and the unconstrained LS problems, respectively, always have exac ..."
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Cited by 1 (1 self)
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Abstract. Recursive Least Squares (RLS) algorithms have widespread applications in many areas, such as realtime signal processing, control and communications. This paper shows that the unique solutions to linearequality constrained and the unconstrained LS problems, respectively, always have exactly the same recursive form. Their only difference lies in the initial values. Based on this, a recursive algorithm for the linearinequality constrained LS problem is developed. It is shown that these RLS solutions converge to the true parameter that satisfies the constraints as the data size increases. A simple and easily implementable initialization of the RLS algorithm is proposed. Its convergence to the exact LS solution and the true parameter is shown. The RLS algorithm, in a theoretically equivalent form by a simple modification, is shown to be robust in that the constraints are always guaranteed to be satisfied no matter how large the numerical errors are. Numerical examples are provided to demonstrate the validity of the above results. 1. Introduction. The least squares (LS) approach has widespread applications in many fields, such as statistics, numerical analysis, and engineering. Its greatest progress in the 20th century was the development of the recursive least squares (RLS) algorithm, which has made the LS method one of the few most important and
On the Solution of Constrained and Weighted Linear Least Squares Problems
, 2005
"... Important problems in many scientific computational areas are least squares problems. The problem of constraint least squares with full column weight matrix is a class of these problems. In this presentation, we are concerned with the connection between the condition numbers and the rounding error i ..."
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Important problems in many scientific computational areas are least squares problems. The problem of constraint least squares with full column weight matrix is a class of these problems. In this presentation, we are concerned with the connection between the condition numbers and the rounding error in the solution of the problem of constrained and weighted linear least squares. The fact that this problem is an intrinsic feature of least squares problems makes it necessary to study the characteristics of its solution. Investigation of the theoretical characteristics of the solution of our problem is based on perturbing the problem and driving bounds for the relative error. Explicit expressions for the inverse and MoorePenrose inverse are used to estimate these bounds. Moreover, the effects of weights are presented. AMS classification: Primary 65F15; Secondary 65G05 Key words and phrases: least squares problems, perturbation, weights.