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Algorithm XXX: Fortran Subroutines for Computing the Eigenvalues and Eigenvectors of a General Matrix by Reduction to General Tridiagonal Form
, 1993
"... . This paper describes programs to reduce a nonsymmetric matrix to tridiagonal form, compute the eigenvalues of the tridiagonal matrix, improve the accuracy of an eigenvalue, and compute the corresponding eigenvector. The intended purpose of the software is to find a few eigenpairs of a dense nonsym ..."
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. This paper describes programs to reduce a nonsymmetric matrix to tridiagonal form, compute the eigenvalues of the tridiagonal matrix, improve the accuracy of an eigenvalue, and compute the corresponding eigenvector. The intended purpose of the software is to find a few eigenpairs of a dense
A survey of generalpurpose computation on graphics hardware
, 2007
"... The rapid increase in the performance of graphics hardware, coupled with recent improvements in its programmability, have made graphics hardware acompelling platform for computationally demanding tasks in awide variety of application domains. In this report, we describe, summarize, and analyze the l ..."
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Cited by 545 (18 self)
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the main body of this report at two separate audiences. First, we describe the techniques used in mapping generalpurpose computation to graphics hardware. We believe these techniques will be generally useful for researchers who plan to develop the next generation of GPGPU algorithms and techniques. Second
LSQR: An Algorithm for Sparse Linear Equations and Sparse Least Squares
 ACM Trans. Math. Software
, 1982
"... An iterative method is given for solving Ax ~ffi b and minU Ax b 112, where the matrix A is large and sparse. The method is based on the bidiagonalization procedure of Golub and Kahan. It is analytically equivalent to the standard method of conjugate gradients, but possesses more favorable numerica ..."
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Cited by 649 (21 self)
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numerical properties. Reliable stopping criteria are derived, along with estimates of standard errors for x and the condition number of A. These are used in the FORTRAN implementation of the method, subroutine LSQR. Numerical tests are described comparing I~QR with several other conjugate
On Computing an Eigenvector of a Tridiagonal Matrix
, 1995
"... We consider the solution of the homogeneous equation (J \Gamma I)x = 0 where J is a tridiagonal matrix, is a known eigenvalue, and x is the unknown eigenvector corresponding to . Since the system is underdetermined, x could be obtained by setting x k = 1 and solving for the rest of the elements o ..."
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Cited by 18 (2 self)
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We consider the solution of the homogeneous equation (J \Gamma I)x = 0 where J is a tridiagonal matrix, is a known eigenvalue, and x is the unknown eigenvector corresponding to . Since the system is underdetermined, x could be obtained by setting x k = 1 and solving for the rest of the elements
Bundle Adjustment  A Modern Synthesis
 VISION ALGORITHMS: THEORY AND PRACTICE, LNCS
, 2000
"... This paper is a survey of the theory and methods of photogrammetric bundle adjustment, aimed at potential implementors in the computer vision community. Bundle adjustment is the problem of refining a visual reconstruction to produce jointly optimal structure and viewing parameter estimates. Topics c ..."
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Cited by 555 (12 self)
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This paper is a survey of the theory and methods of photogrammetric bundle adjustment, aimed at potential implementors in the computer vision community. Bundle adjustment is the problem of refining a visual reconstruction to produce jointly optimal structure and viewing parameter estimates. Topics
FastMap: A Fast Algorithm for Indexing, DataMining and Visualization of Traditional and Multimedia Datasets
, 1995
"... A very promising idea for fast searching in traditional and multimedia databases is to map objects into points in kd space, using k featureextraction functions, provided by a domain expert [25]. Thus, we can subsequently use highly finetuned spatial access methods (SAMs), to answer several types ..."
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Cited by 497 (23 self)
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domain expert to assess the similarity/distance of two objects. Given only the distance information though, it is not obvious how to map objects into points. This is exactly the topic of this paper. We describe a fast algorithm to map objects into points in some kdimensional space (k is user
On Computing an Eigenvector of a Tridiagonal Matrix
"... We consider the solution of the homogeneous equation (J; I)x = 0 where J is a tridiagonal matrix, is a known eigenvalue, and x is the unknown eigenvector corresponding to. Since the system is underdetermined, x could be obtained by setting xk = 1 and solving for the rest of the elements of x. This ..."
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We consider the solution of the homogeneous equation (J; I)x = 0 where J is a tridiagonal matrix, is a known eigenvalue, and x is the unknown eigenvector corresponding to. Since the system is underdetermined, x could be obtained by setting xk = 1 and solving for the rest of the elements of x
The Ensemble Kalman Filter: theoretical formulation And Practical Implementation
, 2003
"... The purpose of this paper is to provide a comprehensive presentation and interpretation of the Ensemble Kalman Filter (EnKF) and its numerical implementation. The EnKF has a large user group, and numerous publications have discussed applications and theoretical aspects of it. This paper reviews the ..."
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Cited by 482 (4 self)
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the important results from these studies and also presents new ideas and alternative interpretations which further explain the success of the EnKF. In addition to providing the theoretical framework needed for using the EnKF, there is also a focus on the algorithmic formulation and optimal numerical
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