The QLY least-squares and the QLY least-squares minimal-norm of linear dual least squares problems
Hongxing Wang, Chong Cui, Yimin Wei
Abstract
In this paper, we define a QLY total order ≤Q over Dm to compare the magnitude of dual vectors. Then we consider the QLY least-squares problem and give its compact formula. Meanwhile, by comparing with a least-squares and the least-squares minimal-norm solutions, we can investigate a QLY least-squares and the QLY least-squares minimal-norm of linear dual least-squares problems. In particular, in the presence of a least-squares solution, we can get a QLY least-squares solution to be more accurate than a least-squares solution under the QLY total order.
Topics & Concepts
Total least squaresMathematicsNon-linear least squaresLeast-squares function approximationIteratively reweighted least squaresGeneralized least squaresLinear least squaresNorm (philosophy)Recursive least squares filterExplained sum of squaresLack-of-fit sum of squaresLeast trimmed squaresResidual sum of squaresApplied mathematicsStatisticsAlgorithmLinear modelRegressionAdaptive filterLawPolitical scienceEstimatorMatrix Theory and AlgorithmsAdvanced Optimization Algorithms ResearchStatistical and numerical algorithms