3 edition of **Complete orthogonal decomposition for weighted least squares** found in the catalog.

Complete orthogonal decomposition for weighted least squares

Patricia D. Hough

- 78 Want to read
- 8 Currently reading

Published
**1994**
by Cornell Theory Center, Cornell University in Ithaca, N.Y
.

Written in English

**Edition Notes**

Statement | Patricia D. Hough, Stephen A. Vavasis. |

Series | Technical report / Cornell Theory Center -- CTC94TR203., Technical report (Cornell Theory Center) -- 203. |

Contributions | Vavasis, Stephen A., Cornell Theory Center. |

The Physical Object | |
---|---|

Pagination | 19 p. ; |

Number of Pages | 19 |

ID Numbers | |

Open Library | OL17007240M |

OCLC/WorldCa | 34092331 |

SVD Decomposition. For any matrix A2Rm nthere exist orthogonal matrices U2R m, V 2R nand a ’diagonal’ matrix 2Rm n, i.e., 0 B B B B B B B B @ ˙ 1 0 r 0 0 1 C C C C C C C C A for m n with diagonal entries ˙ 1 ˙ r>˙ r+1 = = ˙ minfm;ng= 0 such that A= U VT D. Leykekhman - MATH Introduction to Computational MathematicsLinear Least Squares { 2. Weighted Singular Value Decomposition of Matrices with Singular Weights Based on Weighted Orthogonal Transformations Article in Cybernetics and Systems Analysis 51(4) .

Computing the Singular Value Decomposition | MIT SC Linear Algebra, Fall - Duration: MIT OpenCourseWare , views. Now "using orthogonal decomposition" I'm to obtain H'=$\textbf{QU}$, where $\textbf{Q}$ is an (n-1)x(n-1) orthogonal matrix and $\textbf{U}$, which is an (n-1)xn upper diagonal matrix. I guess I'm hoping someone can better explain orthogonal decomposition and help me write the elements of $\textbf{Q}$ and $\textbf{U}$ in terms of the elements.

A note on Constrained Total Least-Squares estimation. the proper orthogonal decomposition has been independently rediscovered several times from different points of view. Weighted total. One could also do weighted least squares as an application, within the context of Sections and , inner product spaces and orthogonal vectors. The presentation of singular value decomposition in Meyer’s book does not use the notions of eigenvalues and eigenvectors, leading to .

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This paper proposes a complete orthogonal decomposition (COD) algorithm for solving weighted least-squares problems. In applications, the weight matrix can be highly ill conditioned, and this can cause standard methods like QR factorization to return inaccurate answers in floating-point by: complete orthogonal decomposition weighted least square least-squares problem accurate solution nsh method nsh algorithm new definition full-rank weighted least-squares problem problem min y2r kd gamma1 standard method weight matrix new algorithm symmetric positive definite theta matrix norm bound ay gamma nullspace method qr factorization.

Abstract. Consider a full-rank weighted least-squares problem in which the weight matrix is highly ill-conditioned. Because of the ill-conditioning, standard methods for solving least-squares problems, QR factorization and the nullspace method for example, break down. Stewart established a norm bound for such a system of equations, indicating that it may be possible to find an algorithm.

Complete Orthogonal Decomposition for Weighted Least Squares. By Patricia D. Hough and Stephen A. Vavasis. Abstract. Consider a full-rank weighted least-squares problem in which the weight matrix is highly ill-conditioned.

Because of the ill-conditioning, standard methods for solving least-squares problems, QR factorization and the nullspace Author: Patricia D.

Hough and Stephen A. Vavasis. A direct algorithm known as Complete Orthogonal Decomposition was proposed by Hough and Vavasis =-=[8-=-]. This method applies to the weighted least squares problem associated with faulted DC power networks.

However, the method relies on the system being real and positive denite. There is. Complete Orthogonal Decomposition for Weighted Least Squares. By Patricia Hough and Stephen A. Vavasis. Abstract. Consider a full-rank weighted least-squares problem in which the weight matrix is highly ill-conditioned.

Because of the ill-conditioning, standard methods for solving least-squares problems, QR factorization and the nullspace. Complete Orthogonal Decomposition for Weighted Least Squares. By Patricia D. Hough and Stephen A.

Vavasis. Abstract. Consider a full-rank weighted least squares problem in which the weight matrix is highly ill-conditioned. Because of the ill-conditioning, standard methods for solving least-squares problems, QR factorization and the nullspace Author: Patricia D.

Hough and Stephen A. Vavasis. GNU Scientific Library Complete Orthogonal Decomposition; Singular Value Decomposition; Cholesky Decomposition; Weighted Nonlinear Least-Squares; Tunable Parameters; Initializing the Solver; Providing the Function to be Minimized; Iteration; Testing for Convergence; High Level Driver.

() Complete Orthogonal Decomposition for Weighted Least Squares. SIAM Journal on Matrix Analysis and ApplicationsAbstract | PDF ( KB)Cited by: Theorem. (The Orthogonal Decomposition Theorem) Let W be a subspace of Rn.

Then each y in Rn can be uniquely represented in the form where is in W and is in In fact, if is any orthogonal basis for W, then and The vector is called the orthogonal projection of y onto Size: KB. Algorithms for the Weighted Orthogonal Procrustes Problem and other Least Squares Problems Thomas Viklands Ph.D.

Thesis, UMINF Department of Computing Science Ume˚a University SE 87 Ume˚a, Sweden Akademisk avhandling som med tillst˚and av. This book is meant to provide an introduction to vectors, matrices, and least squares methods, basic topics in applied linear algebra.

Our goal is to give the beginning student, with little or no prior exposure to linear algebra, a good ground-ing in the basic ideas, as well. The Orthogonal Decomposition Theorem The Orthogonal Decomposition: Example Geometric Interpretation of Orthogonal Projections The Best Approximation Theorem The Best Approximation Theorem: Example New View of Matrix Multiplication Orthogonal Projection: Theorem Jiwen He, University of Houston MathLinear Algebra 2 / 16File Size: KB.

[−1,1]. The method uses the discrete orthogonal polynomial least squares (DOP-LS) ap-proximation based on the super Gaussian weight function, which is both smoothly con-nected to zero at ±1 and equals one in nearly the entire domain. As a result, the method has fast decaying expansion coefﬁcients and also successfully suppresses Runge oscil-Cited by: The minimal least squares solutions is a topic of interest due to the broad range of applications of this problem.

Although it can be obtained from other algorithms, such as the Singular Value Decomposition (SVD) or the Complete Orthogonal Decomposition (COD), the use of LDU factorizations has its advantages, namely the computational cost and the low fill-in that can be obtained using this : I.

Fernández de Bustos, V. García-Marina, G. Urkullu, M. Abasolo. In this paper we employ Householder transformations and compound Givens rotations to compute the Complete Orthogonal Decomposition of a rectangular matrix, using a SIMD array processor. Algorithms are proposed for the reconstruction of the orthogonal matrices involved in the decompositions and the estimated execution time of all parallel Cited by: 4.

This function finds the least squares solution to the overdetermined system where the matrix A has more rows than columns.

The least squares solution minimizes the Euclidean norm of the residual.The routine requires as input the decomposition of into (QR, tau) given by gsl_linalg_QR_decomp(). The solution is returned in x. 2 Chapter 5. Least Squares The symbol ≈ stands for “is approximately equal to.” We are more precise about this in the next section, but our emphasis is on least squares approximation.

The basis functions ϕj(t) can be nonlinear functions of t, but the unknown parameters, βj, appear in the model system of linear equationsFile Size: KB. 4 Total Least Squares 15 5 Bibliography 18 1 The Singular Value Decomposition The singular value decomposition (SVD) of a matrix Ais very useful in the context of least squares problems.

It also very helpful for analyzing properties of a matrix. With the SVD one x-rays a matrix. Theorem (The Singular Value Decomposition, SVD).File Size: KB.

Numerical solution of the least squares problem. In order to find the solutionto (16) weuseanorthogonalmatrix Qsuchthat (17) OTF [OO’]F=] FR-] [0J where R is upper triangular. Since the 2-norm is unaffected by orthogonal transformations, (18) 2 argmin jR] [O’y][]2 0 x-OiyJll’ fromwhichit follows that satisfies (19) R2=Oy.

The Use and Misuse of Orthogonal Regression in Linear Errors-in-Variables Models is a weighted orthogonal distance. Let s s ands be the sample variance of the Y 's, The orthogonal regression estimate of slope is — { (s; — + } 1/2 where þ1(OLS) is the ordinary least square slope estimate.

Small sample improvements to this estimator.An Example of Weighted Least-Squares State Estimation State Estimation of an Ac Network Development of Method Typical Results of State Estimation on an AC Network State Estimation by Orthogonal Decomposition The Orthogonal Decomposition Algorithm M.

Gulliksson, P. WedinModifying the QR-decomposition to constrained and weighted linear least squares SIAM J. Matrix Anal. Appl., 13 (), pp. Google Scholar.