An important problem in analysis on fractals is the existence of a self-similar energy finitely ramified fractals. The energies are constructed terms eigenforms, that is, eigenvectors special nonlinear operator. Previous results by C. Sabot and V. Metz give conditions for an eigenform. In this paper, I prove type result different way. proof given paper based general fixed-point theorem anti-att...

Many problems in machine learning and statistics can be formulated as (generalized) eigenproblems. In terms of the associated optimization problem, computing linear eigenvectors amounts to finding critical points of a quadratic function subject to quadratic constraints. In this paper we show that a certain class of constrained optimization problems with nonquadratic objective and constraints ca...

Spectral methods that are based on eigenvectors and eigenvalues of discrete graph Laplacians, such as DiffusionMaps and Laplacian Eigenmaps, are often used for manifold learning and nonlinear dimensionality reduction. It was previously shown by Belkin&Niyogi (2007, Convergence of Laplacian eigenmaps, vol. 19. Proceedings of the 2006 Conference on Advances in Neural Information Processing System...

The Quadratic Finite Element Model Updating Problem (QFEMUP) concerns with updating a symmetric second-order finite element model so that it remains symmetric and the updated model reproduces a given set of desired eigenvalues and eigenvectors by replacing the corresponding ones from the original model. Taking advantage of the special structure of the constraint set, it is first shown that the ...

Spectral methods for manifold learning and clustering typically construct a graph weighted with affinities (e.g. Gaussian or shortest-path distances) from a dataset and compute eigenvectors of a graph Laplacian. With large datasets, the eigendecomposition is too expensive, and is usually approximated by solving for a smaller graph defined on a subset of the points (landmarks) and then applying ...

The Matrix Model Updating Problem (MMUP), considered in this paper, concerns updating a symmetric second-order finite element model so that the updated model reproduces a given set of desired eigenvalues and eigenvectors by replacing the corresponding ones from the original model, and preserves the symmetry of the original model. In an optimization setting, this is a constrained nonlinear optim...