Capítulos (Instituto de Matemáticas de la Universidad de Sevilla (Antonio de Castro Brzezicki))

URI permanente para esta colecciónhttps://hdl.handle.net/11441/10980

Examinar

Envíos recientes

Mostrando 1 - 1 de 1
  • Miniatura
    Acceso AbiertoCapítulo de Libro
    Low rank approximation of multidimensional data
    (Springer, 2019) Azaïez, Mejdi; Lestandi, Lucas; Chacón Rebollo, Tomás; Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico; Universidad de Sevilla. FQM120: Modelado Matemático y Simulación de Sistemas Medioambientales
    In the last decades, numerical simulation has experienced tremendous improvements driven by massive growth of computing power. Exascale computing has been achieved this year and will allow solving ever more complex problems. But such large systems produce colossal amounts of data which leads to its own difficulties. Moreover, many engineering problems such as multiphysics or optimisation and control, require far more power that any computer architecture could achieve within the current scientific computing paradigm. In this chapter, we propose to shift the paradigm in order to break the curse of dimensionality by introducing decomposition to reduced data. We present an extended review of data reduction techniques and intends to bridge between applied mathematics community and the computational mechanics one. The chapter is organized into two parts. In the first one bivariate separation is studied, including discussions on the equivalence of proper orthogonal decomposition (POD, continuous framework) and singular value decomposition (SVD, discrete matrices). Then, in the second part, a wide review of tensor formats and their approximation is proposed. Such work has already been provided in the literature but either on separate papers or into a pure applied mathematics framework. Here, we offer to the data enthusiast scientist a description of Canonical, Tucker, Hierarchical and Tensor train formats including their approximation algorithms. When it is possible, a careful analysis of the link between continuous and discrete methods will be performed.