• Title/Summary/Keyword: least squares problem

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WorldView-2 pan-sharpening by minimization of spectral distortion with least squares

  • Choi, Myung-Jin
    • Korean Journal of Remote Sensing
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    • v.27 no.3
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    • pp.353-357
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    • 2011
  • Although the intensity-hue-saturation (IHS) method for pan-sharpening has a spectral distortion problem, it is a popular method in the remote sensing community and has been used as a standard procedure in many commercial packages due to its fast computing and easy implementation. Recently, IHS-like approaches have tried to overcome the spectral distortion problem inherited from the IHS method itself and yielded a good result. In this paper, a similar IHS-like method with least squares for WorldView-2 pan-sharpening is presented. In particular, unlike the previous methods with three or four-band multispectral images for pan-sharpening, six bands of WorldView-2 multispectral image located within the range of panchromatic spectral radiance responses are considered in order to reduce the spectral distortion during the merging process. As a result, the new approach provides a satisfactory result, both visually and quantitatively. Furthermore, this shows great value in spectral fidelity of WorldView-2 eight-band multispectral imagery.

Blockwise analysis for solving linear systems of equations

  • Smoktunowicz, Alicja
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.3 no.1
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    • pp.31-41
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    • 1999
  • We investigate some techniques of iterative refinement of solutions of a nonsingular system Ax = b with A partitioned into blocks using only single precision arithmetic. We prove that iterative refinement improves a blockwise measure of backward stability. Some applications of the results for the least squares problem (LS) will be also considered.

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EXPERIMENTAL RESULTS OF W-CYCLE MULTIGRID FOR PLANAR LINEAR ELASTICITY

  • Yoo, Jae-Chil
    • East Asian mathematical journal
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    • v.14 no.2
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    • pp.399-410
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    • 1998
  • In [3], Franca and Stenberg developed several Galerkin least squares methods for the solution of the problem of linear elasticity. That work concerned itself only with the error estimates of the method. It did not address the related problem of finding effective methods for the solution of the associated-linear systems. In this work, we present computational experiments of W-cycle multigrid method. Computational experiments show that the convergence is uniform as the parameter, $\nu$, goes to 1/2.

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GEOMETRIC FITTING OF CIRCLES

  • Kim, Ik-Sung
    • Journal of applied mathematics & informatics
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    • v.7 no.3
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    • pp.983-994
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    • 2000
  • We consider the problem of determining the circle of best fit to a set of data points in the plane. In [1] and [2] several algorithms already have been given for fitting a circle in least squares sense of minimizing the geometric distances to the given data points. In this paper we present another new descent algorithm which computes a parametric represented circle in order to minimize the sum of the squares of the distances to the given points. For any choice of starting values our algorithm has the advantage of ensuring convergence to a local minimum. Numerical examples are given.

Approximate Optimization Using Moving Least Squares Response Surface Methods: Application to FPSO Riser Support Design

  • Song, Chang-Yong;Lee, Jong-Soo;Choung, Joon-Mo
    • Journal of Ocean Engineering and Technology
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    • v.24 no.1
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    • pp.20-33
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    • 2010
  • The paper deals with strength design of a riser support installed on floating production storage and offloading (FPSO) vessel under various loading conditions - operation, extreme, damaged, one line failure case (OLFC) and installation. The design problem is formulated such that thickness sizing variables are determined by minimizing the weight of a riser support structure subject to stresses constraints. The initial design model is generated based on an actual FPSO riser support specification. The finite element analysis (FEA) is conducted using MSC/NASTRAN, and optimal solutions are obtained via moving least squares method (MLSM) in the context of response surface based approximate optimization. For the meta-modeling of inequality constraint functions of stresses, a constraint-feasible moving least squares method (CF-MLSM) is used in the present study. The method of CF-MLSM, compared to a conventional MLSM, has been shown to ensure the constraint feasibility in a case where the approximate optimization process is employed. The optimization results present improved design performances under various riser operating conditions.

Analysis of Moving Boundary Problem Using Extended Moving Least Squares Finite Difference Method (확장된 이동최소제곱 유한차분법을 이용한 이동경계문제의 해석)

  • Yoon, Young-Cheol;Kim, Do-Wan
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.22 no.4
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    • pp.315-322
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    • 2009
  • This paper presents a novel numerical method based on the extended moving least squares finite difference method(MLS FDM) for solving 1-D Stefan problem. The MLS FDM is employed for easy numerical modelling of the moving boundary and Taylor polynomial is extended using wedge function for accurate capturing of interfacial singularity. Difference equations for the governing equations are constructed by implicit method which makes the numerical method stable. Numerical experiments prove that the extended MLS FDM show high accuracy and efficiency in solving semi-infinite melting, cylindrical solidification problems with moving interfacial boundary.

CONDITION NUMBERS WITH THEIR CONDITION NUMBERS FOR THE WEIGHTED MOORE-PENROSE INVERSE AND THE WEIGHTED LEAST SQUARES SOLUTION

  • Kang Wenhua;Xiang Hua
    • Journal of applied mathematics & informatics
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    • v.22 no.1_2
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    • pp.95-112
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    • 2006
  • In this paper, the authors investigate the condition number with their condition numbers for weighted Moore-Penrose inverse and weighted least squares solution of min /Ax - b/M, where A is a rank-deficient complex matrix in $C^{m{\times}n} $ and b a vector of length m in $C^m$, x a vector of length n in $C^n$. For the normwise condition number, the sensitivity of the relative condition number itself is studied, the componentwise perturbation is also investigated.

A Recursive Data Least Square Algorithm and Its Channel Equalization Application

  • Lim, Jun-Seok;Kim, Jae-Soo
    • The Journal of the Acoustical Society of Korea
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    • v.25 no.2E
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    • pp.43-48
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    • 2006
  • Abstract-Using the recursive generalized eigendecomposition method, we develop a recursive form solution to the data least squares (DLS) problem, in which the error is assumed to lie in the data matrix only. Simulations demonstrate that DLS outperforms ordinary least square for certain types of deconvolution problems.

Biased-Recovering Algorithm to Solve a Highly Correlated Data System (상관관계가 강한 독립변수들을 포함한 데이터 시스템 분석을 위한 편차 - 복구 알고리듬)

  • 이미영
    • Journal of the Korean Operations Research and Management Science Society
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    • v.28 no.3
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    • pp.61-66
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    • 2003
  • In many multiple regression analyses, the “multi-collinearity” problem arises since some independent variables are highly correlated with each other. Practically, the Ridge regression method is often adopted to deal with the problems resulting from multi-collinearity. We propose a better alternative method using iteration to obtain an exact least squares estimator. We prove the solvability of the proposed algorithm mathematically and then compare our method with the traditional one.

A Robust Estimation Procedure for the Linear Regression Model

  • Kim, Bu-Yong
    • Journal of the Korean Statistical Society
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    • v.16 no.2
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    • pp.80-91
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    • 1987
  • Minimum $L_i$ norm estimation is a robust procedure ins the sense that it leads to an estimator which has greater statistical eficiency than the least squares estimator in the presence of outliers. And the $L_1$ norm estimator has some desirable statistical properties. In this paper a new computational procedure for $L_1$ norm estimation is proposed which combines the idea of reweighted least squares method and the linear programming approach. A modification of the projective transformation method is employed to solve the linear programming problem instead of the simplex method. It is proved that the proposed algorithm terminates in a finite number of iterations.

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