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A proximal ANLS algorithm for nonnegative tensor factorization with a periodic enhanced line search

Douglas Bunker, Lixing Han, Shu Hua Zhang (2013)

Applications of Mathematics

The Alternating Nonnegative Least Squares (ANLS) method is commonly used for solving nonnegative tensor factorization problems. In this paper, we focus on algorithmic improvement of this method. We present a Proximal ANLS (PANLS) algorithm to enforce convergence. To speed up the PANLS method, we propose to combine it with a periodic enhanced line search strategy. The resulting algorithm, PANLS/PELS, converges to a critical point of the nonnegative tensor factorization problem under mild conditions....

Alcune osservazioni sul rango numerico per operatori non lineari

Jürgen Appell, G. Conti, Paola Santucci (1999)

Mathematica Bohemica

We discuss some numerical ranges for Lipschitz continuous nonlinear operators and their relations to spectral sets. In particular, we show that the spectrum defined by Kachurovskij (1969) for Lipschitz continuous operators is contained in the so-called polynomial hull of the numerical range introduced by Rhodius (1984).

Computation of bifurcated branches in a free boundary problem arising in combustion theory

Olivier Baconneau, Claude-Michel Brauner, Alessandra Lunardi (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We consider a parabolic 2D Free Boundary Problem, with jump conditions at the interface. Its planar travelling-wave solutions are orbitally stable provided the bifurcation parameter u * does not exceed a critical value u * c . The latter is the limit of a decreasing sequence ( u * k ) of bifurcation points. The paper deals with the study of the 2D bifurcated branches from the planar branch, for small k. Our technique is based on the elimination of the unknown front, turning the problem into a fully nonlinear...

Métodos para la actualización de los factores de Q y R de una matriz.

Laureano F. Escudero (1984)

Trabajos de Estadística e Investigación Operativa

Recientemente se han propuesto varios métodos para modificar los factores Q y R de una matriz una vez que se ha eliminado (o añadido) una fila o una columna. Normalmente la descripción de estos métodos se efectúa en el contexto de una determinada aplicación; quizá sea ésta la causa de su escasa difusión.

Nonsingularity and P -matrices.

Jiří Rohn (1990)

Aplikace matematiky

New proofs of two previously published theorems relating nonsingularity of interval matrices to P -matrices are given.

On the generalized Riccati matrix differential equation. Exact, approximate solutions and error estimate

Lucas Jódar, Enrique A. Navarro (1989)

Aplikace matematiky

In this paper explicit expressions for solutions of Cauchy problems and two-point boundary value problems concerned with the generalized Riccati matrix differential equation are given. These explicit expressions are computable in terms of the data and solutions of certain algebraic Riccati equations related to the problem. The interplay between the algebraic and the differential problems is used in order to obtain approximate solutions of the differential problem in terms of those of the algebraic...

Replicant compression coding in Besov spaces

Gérard Kerkyacharian, Dominique Picard (2010)

ESAIM: Probability and Statistics

We present here a new proof of the theorem of Birman and Solomyak on the metric entropy of the unit ball of a Besov space B π , q s on a regular domain of d . The result is: if s - d(1/π - 1/p)+> 0, then the Kolmogorov metric entropy satisfies H(ε) ~ ε-d/s. This proof takes advantage of the representation of such spaces on wavelet type bases and extends the result to more general spaces. The lower bound is a consequence of very simple probabilistic exponential inequalities. To prove the upper bound,...

Replicant compression coding in Besov spaces

Gérard Kerkyacharian, Dominique Picard (2003)

ESAIM: Probability and Statistics

We present here a new proof of the theorem of Birman and Solomyak on the metric entropy of the unit ball of a Besov space B π , q s on a regular domain of d . The result is: if s - d ( 1 / π - 1 / p ) + > 0 , then the Kolmogorov metric entropy satisfies H ( ϵ ) ϵ - d / s . This...

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