Cover of: Supremum and Stability of Weighted Pseudoinverses and Weighted Least Squares Problems | Musheng Wei

Supremum and Stability of Weighted Pseudoinverses and Weighted Least Squares Problems

Analysis and Computations
  • 182 Pages
  • 2.28 MB
  • 8813 Downloads
  • English
by
Nova Science Publishers
Computers, Mathematics, Computer Books: General, General, Computer Science, Least squares, Pseudoinv
The Physical Object
FormatHardcover
ID Numbers
Open LibraryOL12120195M
ISBN 101560729228
ISBN 139781560729228

Forsgren further generalized these results to derive the supremum of weighted pseudoinverses sup ‖(W W ∈P 1 2 X) + W 1 2 ‖2 where P is a set of diagonally dominant positive semidefinite matrices, by using a signature decomposition of weighting matrices W and by applying the Binet-Cauchy formula and Cramer’s rule for determinants.

We improved their results to obtain the supremum of scaled pseudoinverses and derived the stability property of scaled pseudoinverses. Forsgren further generalized these results to derive the supremum of weighted pseudoinverses sup W2P k(W 1 2 X) + W 1 2 k 2 where P is a set of diagonally dominant positive semidefinite matrices, by using a.

set of Eq. (1) is close to a related multi- level constrained least squares problem. Based on this observation, Wei [18] derived the stability conditions of perturbed stiff weighted pseudoinverses and stiff WLS problems. Without loss of generality, we make the following notation and assumptions for the matrices A and W.

Assumption The monograph mainly contains the following three parts: analysis of supremum of weighted pseudoinverses, study the stability of weighted pseudoinverses, weighted least squares problems and constrained weighted least squares problems, and stable methods for solving weighted least squares problems and constrained weighted least squares : Musheng Wei.

At each iteration step for solving mathematical programming and constrained optimization problems by using interior-point methods, one often needs to solve the weighted least squares (WLS) problem.

Description Supremum and Stability of Weighted Pseudoinverses and Weighted Least Squares Problems FB2

Supremum and stability of Supremum and Stability of Weighted Pseudoinverses and Weighted Least Squares Problems book pseudoinverses and weighted least squares problems. this paper we consider solving a sequence of weighted linear least squares problems where the only.

() Stability of the MGS-like elimination method for equality constrained least squares problems. Journal of Shanghai University (English Edition)() Inverse Fault Detection and Diagnosis Problem in Discrete Dynamic Systems.

A weighted least squares problem {ie} with positive definite weights M and N is considered, where A ∈ R m×n is a rank-deficient matrix, b ∈ R hereditary, computational, and global errors of a weighted normal pseudosolution are estimated for perturbed initial data, including the case where the rank of the perturbed matrix varies.

M.

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Wei, Supremum and Stability of Weighted Pseudoinverses and Weighted Least Squares Problems Analysis and Computations (Nova Science Publisher Inc., Huntington, ) zbMATH Google Scholar Y. Wei, G. Wang, On continuity of the generalized inverse \(A_{T, S}^{(2)}\).

Supremum and stability of weighted pseudoinverses and weighted least squares problems, Analysis and computations,Nova Science Publishers, Inc., Huntington, NY () xiv+ pp Google Scholar. Let A ∈ R m×n be a full column rank matrix. The chi measure χ(A) arises naturally in weighted least-squares problems of the form min D 1/2 (Ax − b) 2, see, e.g., [4,9, 10, 18].

The chi. Equivalent formulae for the supremum and stability of weighted pseudoinverses. Author: Musheng Wei Forsgren further generalized these results to derive the supremum of weighted pseudoinverses where is a set of diagonally Algebraic properties of the rank-deficient equality-constrained and weighted least squares problems, Linear.

The weighted pseudoinverse providing the minimum semi-norm solution of the weighted linear least squares problem is studied. It is shown that it has properties analogous to those of the Moore-Penrose pseudoinverse.

The relation between the weighted pseudoinverse and generalized singular values is explained. The weighted pseudoinverse theory is used to analyse least squares problems with.

Wei, Supremum and Stability of Weighted Pseudoinverses and Weighted Least Squares Problems: Analysis and Computations (Huntington, New York, ).

zbMATH Google Scholar D. Wang, “Some Topics on Weighted Moore-Penrose Inverse, Weighted Least Squares, and Weighted Regularized Tikhonov Problems,” Appl. Math. Comput.

stability of the problems when the diagonal elements of the weight matrix W vary widely in size. Such a situation occurs when solving the WLSE problem by the method of weighting [1,2,31], or solving the constrained optimization problems by interior point methods. The authors of [15,22,29,36,37]study the supremum of weighted pseudoinverses.

Displacement Structure of Weighted Pseudoinverses ∗ Jianfeng Cai 1 Yimin Wei 2 1 Institute of Mathematics, Fudan University, Shanghai, ,PR China. 2 Department of Mathematics, Fudan University, Shanghai, ,PR China.

Details Supremum and Stability of Weighted Pseudoinverses and Weighted Least Squares Problems PDF

E-mail: [email protected] Abstract Estimates for the rank of A† MN V− UA † MN and more general displacement of A MN are presented,where A†.

In this paper, some new properties of the equality constrained and weighted least squares problem (WLSE) min ∥W 1/2 (Kx−g)∥ 2 subject to Lx=h are obtained. We derive a perturbation bound based on an unconstrained least squares problem and deduce some equivalent formulae for the projectors of this unconstrained LS problem.

() Perturbation bounds for constrained and weighted least squares problems. Linear Algebra and its Applications() Some new properties of the equality constrained and weighted least squares problem.

Supremum and stability of weighted pseudoinverses and weighted least squares problems. The main body of the book remains unchanged from the original book. Wei, Supremum and Stability of Weighted Pseudoinverses and Weighted Least Squares Problems Analysis and Computations (Nova Science Publisher Inc, Huntington, NY, ) zbMATH Google Scholar L.

Eldén, A weighted pseudoinverse, generalized singular values and constrained least squares problems. () Mixed and component wise condition numbers for weighted Moore-Penrose inverse and weighted least squares problems. Filomat. () Frequency domain weighted nonlinear least squares estimation of parameter-varying differential equations.

Automat () Optimizing synchronization stability of the Kuramoto model in complex networks and power grids. The studies [6][7] [8] use singular value decomposition of matrices to analyze the influence of perturbations of input data on the solutions of least squares problems and [9] obtains weighted.

Equivalent formulae for the supremum and stability of weighted pseudoinverses Musheng Wei. Math. Comp. 66 (), Abstract, references and article information Full-text PDF Free Access Request permission to use this material MathSciNet review: 1 Weighted Least Squares 1 2 Heteroskedasticity 3 Weighted Least Squares as a Solution to Heteroskedasticity 5 3 Local Linear Regression 10 4 Exercises 15 1 Weighted Least Squares Instead of minimizing the residual sum of squares, RSS() = Xn i=1 (y i ~x i)2 (1) we could minimize the weighted sum of squares, WSS(;w~) = Xn i=1 w i(y.

M. Wei, Supremum and Stability of Weighted Pseudoinverses and Weighted Least Squares Prob- lems: Analysis and Computations, Nova Science Publisher, [39] M. Wei, A.R. De Pierro, Upper perturbation bounds of weighted projections, weighted and con- strained least squares problems, SIAM J.

Matrix Anal. Appl. 21 (3) () – [40] R. Highlights For weighted linear least squares problems, effective condition numbers Cond_eff are explored. The extremely accurate leading coefficient of Motz's problem is explained by very small Cond_eff.

The effective condition number may become a new trend of stability analysis of. Until now there has not been a monograph that covers the full spectrum of relevant problems and methods in least squares. This volume gives an in-depth treatment of topics such as methods for sparse least squares problems, iterative methods, modified least squares, weighted problems, and constrained and regularized problems.

In this paper, we present characterizations for the level-2 condition number of the weighted Moore–Penrose inverse, i.e., cond M N (A) ≤ cond M N [2] (A) ≤ cond M N (A) + 1, where cond M N (A) is the condition number of the weighted Moore–Penrose inverse of a rectangular matrix and cond M N [2] (A) is the level-2 condition number of this problem.

This paper extends the result by. the supremum of this set exists in X(by the least upper bound property of X). It is then straight-forward to verify that this is the in mum of S. First, de ne L= f 2Xj x; for all x2Sg.

We have that Lis nonempty because S is bounded below. Since L X and Lis bounded above (by S), it follows that sup(L) 2Xby the least upper bound property of X. Lecture 24{ Weighted and Generalized Least SquaresFallSection B 19 and 24 November Contents 1 Weighted Least Squares 2 2 Heteroskedasticity 4 Weighted Least Squares as a Solution to Heteroskedasticity Some Explanations for Weighted Least Squares 3 The Gauss-Markov Theorem To test for a difference in the effects of different induction and maintenance treatment combinations, a modified supremum weighted log-rank test is proposed.

The test is applied to a dataset from a two-stage randomized trial and the results are compared to those obtained using a standard weighted .pooling of variance, weighted average, weighted least squares regression.

1. Introduction e purpose of this article is to discuss the problem of calculating "best" estimates from a series of experimen-tal results.

It will be convenient to refer to these estimates as consensus values. Since experimental data.