Extension de la méthode Procuste à la comparaison de nuages de points situés dans des espaces de dimensions différentes
Falseness of the finiteness property of the spectral subradius
We prove that there exist infinitely may values of the real parameter α for which the exact value of the spectral subradius of the set of two matrices (one matrix with ones above and on the diagonal and zeros elsewhere, and one matrix with α below and on the diagonal and zeros elsewhere, both matrices having two rows and two columns) cannot be calculated in a finite number of steps. Our proof uses only elementary facts from the theory of formal languages and from linear algebra, but it is not constructive...
Fiedler vectors with unbalanced sign patterns
In spectral bisection, a Fielder vector is used for partitioning a graph into two connected subgraphs according to its sign pattern. We investigate graphs having Fiedler vectors with unbalanced sign patterns such that a partition can result in two connected subgraphs that are distinctly different in size. We present a characterization of graphs having a Fiedler vector with exactly one negative component, and discuss some classes of such graphs. We also establish an analogous result for regular graphs...
Filter factors of truncated TLS regularization with multiple observations
The total least squares (TLS) and truncated TLS (T-TLS) methods are widely known linear data fitting approaches, often used also in the context of very ill-conditioned, rank-deficient, or ill-posed problems. Regularization properties of T-TLS applied to linear approximation problems were analyzed by Fierro, Golub, Hansen, and O’Leary (1997) through the so-called filter factors allowing to represent the solution in terms of a filtered pseudoinverse of applied to . This paper focuses on the situation...
Fine spectra of tridiagonal symmetric matrices.
Fixed points of rotations of -sphere.
Further results on the Craig-Sakamoto equation.
Gegenbauer polynomials and semiseparable matrices.
Generalization of the Bauer-Fike Theorem.
Generalized approximation numbers
Generalized Catalan numbers. (Nombres de Catalan généralisés.)
Geometric aspects of linear transformations of the plane.
Graphs determined by their (signless) Laplacian spectra.
Guided Local Search for query reformulation using weight propagation
A new technique for query reformulation that assesses the relevance of retrieved documents using weight propagation is proposed. The technique uses a Guided Local Search (GLS) in conjunction with the latent semantic indexing model (to semantically cluster documents together) and Lexical Matching (LM). The GLS algorithm is used to construct a minimum spanning tree that is later employed in the reformulation process. The computations done for Singular Value Decomposition (SVD), LM and the minimum...
Hadamard product versions of the Chebyshev and Kantorovich inequalities.
Harmonic Rayleigh-Ritz extraction for the multiparameter eigenvalue problem.
Improved upper bounds for the Laplacian spectral radius of a graph.
Improving backward stability of Sakurai-Sugiura method with balancing technique in polynomial eigenvalue problem
One of the most efficient methods for solving the polynomial eigenvalue problem (PEP) is the Sakurai-Sugiura method with Rayleigh-Ritz projection (SS-RR), which finds the eigenvalues contained in a certain domain using the contour integral. The SS-RR method converts the original PEP to a small projected PEP using the Rayleigh-Ritz projection. However, the SS-RR method suffers from backward instability when the norms of the coefficient matrices of the projected PEP vary widely. To improve the backward...
Inclusion Theorems for a Section of a Matrix.
Indecomposable matrices over a distributive lattice
In this paper, the concepts of indecomposable matrices and fully indecomposable matrices over a distributive lattice are introduced, and some algebraic properties of them are obtained. Also, some characterizations of the set of all fully indecomposable matrices as a subsemigroup of the semigroup of all Hall matrices over the lattice are given.