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A wavelet approach is presented for estimating a partially linear model (PLM). We ÿnd an estimator of the PLM by minimizing the square of the l2 norm of the residual vector while penalizing the l1 norm of the wavelet coeecients of the nonparametric component. This approach, an extension of the wavelet approach for nonparametric regression problems, avoids… (More)

— A box-constrained integer least squares problem (BILS) arises from several wireless communications applications. Solving a BILS problem usually has two stages: reduction (or preprocessing) and search. This paper presents a reduction algorithm and a search algorithm. Unlike the typical reduction algorithms , which use only the information of the lattice… (More)

This paper gives perturbation analyses for Q 1 and R in the QR factorization A = Q 1 R, Q T 1 Q 1 = I, for a given real m n matrix A of rank n. The analyses more accurately reeect the sensitivity of the problem than previous normwise results. The condition numbers here are altered by any column pivoting used in AP = Q 1 R, and the condition numbers for R… (More)

This paper gives componentwise perturbation analyses for Q and R in the QR factorization A = QR, Q T Q = I, R upper triangular, for a given real m × n matrix A of rank n. Such specific analyses are important for example when the columns of A are badly scaled. First order perturbation bounds are given for both Q and R. The analyses more accurately reflect… (More)

The Global Positioning System (GPS) is a satellite based navigation system. GPS satellites transmit signals that allow one to determine the location of GPS receivers. In GPS, a typical technique for kinematic position estimation is differential positioning where two receivers are used: one receiver is stationary and its exact position is known, and the… (More)

An efficient regularization approach is proposed for decoding underdetermined multiple input multiple output (MIMO) systems. The main idea is to transform an underdetermined integer least squares problem to an equivalent overdetermined integer least squares problem by using part of the transmit vector to do a regularization. Some strategies are proposed to… (More)

When processing observational data, statistical testing is an essential instrument to hopefully render harmless incidental anomalies and disturbances in the measurements. A commonly used test statistic based on the general linear model is the generalized likelihood ratio test statistic. The standard formula given in the literature for this test statistic is… (More)

We explain an interesting property of minimum residual iterative methods for the solution of the linear least squares (LS) problem. Our analysis demonstrates that the stopping criteria commonly used with these methods can in some situations be too conservative, causing any chosen method to perform too many iterations or even fail to detect that an… (More)

In 1982, Arjen Lenstra, Hendrik Lenstra Jr. and László Lovász introduced an efficiently computable notion of reduction of basis of a Euclidean lattice that is now commonly referred to as LLL-reduction. The precise definition involves the R-factor of the QR factorization of the basis matrix. In order to circumvent the use of rational/exact arithmetic with… (More)