Xiao-Wen Chang

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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)
A wavelet approach is presented for estimating a partially linear model (PLM). We find an estimator of the PLM by minimizing the square of the l2 norm of the residual vector with penalizing the l1 norm of the wavelet coefficients of the nonparametric component. This approach, an extension of the wavelet approach for nonparametric regression problems, avoids(More)
A recursive least squares algorithm is presented for short baseline GPS positioning using both carrier phase and code measurements. We take advantage of the structure of the problem to make the algorithm computationally efficient and use orthogonal transformations to ensure that the algorithm is numerically reliable. Details are given for computing position(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)
This article presents rigorous normwise perturbation bounds for the Cholesky, LU, and QR factorizations with normwise or componentwise perturbations in the given matrix. The considered componentwise perturbations have the form of backward rounding errors for the standard factorization algorithms. The used approach is a combination of the classic and refined(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 componentwise perturbation analyses for Q and R in the QR factorization A = QR, QTQ = I , R upper triangular, for a given realm×nmatrixA of rank n. Such specific analyses are important for examplewhen the columns ofA are badly scaled. First order perturbation bounds are given for both Q and R. The analyses more accurately reflect the(More)
In GNSS, for fixing integer ambiguities and estimating positions, a mixed integer least squares problem has to be solved. The MATLAB package MILES provides fast and numerically reliable routines to solve this problem. In the process of solving a mixed integer least squares problem, an ordinary integer least squares problem is solved. Thus this package can(More)