Fast matrix computations for functional additive models

Additive Preconditioning for Matrix Computations

Versus the customary preconditioners, our weakly random ones are generated more readily and for a much larger class of input matrices. Furthermore our preconditioners have a wider range of applications, in particular to linear systems with rectangular and rank deficient coefficient matrices and to eigen-solving. We study the generation of such preconditioners and their impact on conditioning of...

TR-2007003: Additive Preconditioning for Matrix Computations

Multiplicative preconditioning is a popular SVD-based techniques for the solution of linear systems of equations. Our novel SVD-free additive preconditioners are more readily available and better preserve matrix structure. We study their generation and their affect on conditioning of the input matrix. In other papers we combine additive preconditioning with aggregation and other relevant techni...

TR-2008004: Additive Preconditioning for Matrix Computations

Versus the customary preconditioners, our weakly random ones are generated more readily and for a much larger class of input matrices. Furthermore our preconditioners have a wider range of applications, in particular to linear systems with rectangular and rank deficient coefficient matrices and to eigen-solving. We study the generation of such preconditioners and their impact on conditioning of...

Fast Matrix Polynomial Computations

Pour une matrice polynomiale P(x) de degr e d dans Mn;n(Kx]), o u K est un corps commutatif, une r eduction a la forme normale d'Hermite peut ^ etre calcul ee en O ~ (M(nd)) op erations arithm etiques, si M(n) est le co^ ut du produit de deux matrices n n sur K. De plus, une telle r eduction peut ^ etre obtenue en temps parall ele O(log +1 (nd)) en utilisant O(L(nd)) processeurs, si le probl em...

Computations for Linear and Generalized Additive Models