Consider applying the Conjugate Residual (CR) method, which is a Krylov subspace type iterative solver, to systems of linear equations Ax = b or least squares problems min x∈Rn ‖b −Ax‖2, where A is singular and nonsymmetric. We will show that when R(A)⊥ = kerA, the CR method can be decomposed into the R(A) and kerA components, and the necessary and sufficient condition for the CR method to conv...

and Kk(BA,Br) = span{Br, (BA)Br, . . . , (BA)k−1Br}, (3) where B ∈ Rn×m is the mapping and preconditioning matrix, and apply Krylov subspace iteration methods on these subspaces. For overdetermined problems, applying the standard CG method to Kk(BA,Br) leads to the preconditioned CGLS [3] or CGNR [9] method while for underdetermined problems it leads to preconditioned CGNE [9] method. The GMRES...

Quantitative steganalysis aims to estimate the amount of payload in a stego object, and such estimators seem to arise naturally in steganalysis of Least Significant Bit (LSB) replacement in digital images. However, as with all steganalysis, the estimators are subject to errors, and their magnitude seems heavily dependent on properties of the cover. In very recent work we have given the first de...

for an unknown vector of parameters β0 and an unknown univariate function τ(·). This model is implied by many important limited dependent variable and regression models, as discussed in Ruud (1986) and Stoker (1986). Consistent estimators for β0, up to an unknown scale factor, have been developed by Ruud (1986), Stoker (1986), Powell, Stock, and Stoker (1989), Ichimura (1993), and others. In th...

Internal forces in the human body can be estimated from measured movements and external forces using inverse dynamic analysis. Here we present a general method of analysis which makes optimal use of all available data, and allows the use of inverse dynamic analysis in cases where external force data is incomplete. The method was evaluated for the analysis of running on a partially instrumented ...

This work introduces the weighted radial basis collocation method for boundary value problems. We first show that the employment of least-squares functional with quadrature rules constitutes an approximation of the direct collocation method. Standard radial basis collocation method, however, yields a larger solution error near boundaries. The residuals in the least-squares functional associated...

Using the facet model we design a family of filters for the approximation of partial derivatives of the digital image surface. Prior information (e.g., local dominant orientation) are incorporated in a two dimensional weight function. A weighted least squares estimation of the facet parameters is applied in order to design the proposed filters. Exemplary application of the proposed filters to f...

Missing values often exist in the data of gene expression microarray experiments. A number of methods such as the Row Average (RA) method, KNNimpute algorithm and SVDimpute algorithm have been proposed to estimate the missing values. Recently, Kim et al. proposed a Local Least Squares Imputation (LLSI) method for estimating the missing values. In this paper, we propose a Weighted Local Least Sq...

We consider residual-sum-of-squares-based model comparison tests using weighted least squares formulations and asymptotic statistics. An biological example from cell proliferation investigations is presented in some detail to illustrate usefulness of the new results. AMS subject classifications: 34A55, 62F03, 62F12, 93E24.