We calculate the main asymptotic terms for eigenvalues, both simple and multiple, and eigenfunctions of the Neumann Laplacian in a three-dimensional domain Ω(h) perturbed by a small (with diameter O(h)) Lipschitz cavern ωh in a smooth boundary ∂Ω = ∂Ω(0). The case of the hole ωh inside the domain but very close to the boundary ∂Ω is under consideration as well. It is proven that the main correc...

image analysis, feature correspondence, stereo, singular value, decomposition This paper presents a new simple method for achieving feature correspondence across a pair of images which requires no calibration information and draws from the method proposed by Scott and Longuet Higgins [8]. Despite the well-known combinatorial complexity of the problem, this work shows that an acceptably good sol...

In this paper, we explore the application of SVD for collaborative filtering. We employ the incremental SVD method for predicting movie ratings based on previous user preferences using the dataset provided by Netflix. Various experiments are performed to see the effect of different parameters on the performance of the algorithm. The results show that the method has potential, although it is pro...

− The steady state data reconciliation problem is approached via a geometrical picture of its model and measurement abstract spaces. By completely utilizing the structure of the problem constraint matrix, via its singular value decomposition (SVD), data adjustment is accomplished and redundancy and observability conditions are formulated. As an example, the method is applied to a small network ...

An explicit procedure is presented for computing both model and data resolution matrices within a Paige-Saunders LSQR algorithm for iterative inversion in seismic tomography. These methods are designed to avoid the need for an additional singular value decomposition of the ray-path matrix. The techniques discussed are completely general since they are based on the multiplicity of equivalent exa...

A new method for detecting shot boundaries in video sequences using singular value decomposition (SVD) is proposed. The method relies on performing singular value decomposition on the matrix A created from 3D histograms of single frames. We have used SVD for its capabilities to derive a low dimensional refined feature space from a high dimensional raw feature space, where pattern similarity can...

In this paper we perform an analytical and numerical study of Extreme Value distributions in discrete dynamical systems that have a singular measure. Using the block maxima approach described in Faranda et al. [2011] we show that, numerically, the Extreme Value distribution for these maps can be associated to the Generalised Extreme Value family where the parameters scale with the information d...

NOTE: I have not thoroughly proofread these notes!!! We recommend the reader review Weeks 9-11 of Linear Algebra: Foundations to Frontiers-Notes to LAFF With.

In this report, we investigate the truncated multilinear singular value decomposition (MLSVD), proposed in De Lathauwer et al. (2000). Truncating the MLSVD results in an approximation, with a prescribed multilinear rank, to a tensor. We present a new error expression for an approximate Tucker decomposition with orthogonal factor matrices. From this expression, new insights are obtained which le...