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Publications Influence

Implicit standard Jacobi gives high relative accuracy

- F. Dopico, P. Koev, J. M. Molera
- Mathematics, Computer Science
- Numerische Mathematik
- 29 September 2009

TLDR

26 4

Weyl-type relative perturbation bounds for eigensystems of Hermitian matrices

- F. Dopico, J. Moro, J. M. Molera
- Mathematics
- 15 April 2000

We present a Weyl-type relative bound for eigenvalues of Hermitian perturbations A+E of (not necessarily definite) Hermitian matrices A. This bound, given in function of the quantity… Expand

19 4- PDF

Accurate solution of structured linear systems via rank-revealing decompositions

- F. Dopico, J. M. Molera
- Mathematics
- 1 July 2012

Linear systems of equations Ax = b, where the matrix A has some particular structure, arise frequently in applications. Very often structured matrices have huge condition numbers κ(A) = ‖A−1‖‖A‖ and,… Expand

25 3- PDF

Accurate Solution of Structured Least Squares Problems via Rank-Revealing Decompositions

- N. Castro-González, J. Ceballos, F. Dopico, J. M. Molera
- Computer Science, Mathematics
- SIAM J. Matrix Anal. Appl.
- 30 July 2013

TLDR

20 2- PDF

Perturbation Theory for Factorizations of LU Type through Series Expansions

- F. Dopico, J. M. Molera
- Mathematics, Computer Science
- SIAM J. Matrix Anal. Appl.
- 1 June 2005

TLDR

17 1- PDF

An Orthogonal High Relative Accuracy Algorithm for the Symmetric Eigenproblem

- F. Dopico, J. M. Molera, J. Moro
- Mathematics, Computer Science
- SIAM J. Matrix Anal. Appl.
- 1 February 2003

TLDR

32- PDF

MULTIPLICATIVE PERTURBATION THEORY AND ACCURATE SOLUTION OF LEAST SQUARES PROBLEMS

Least squares problems minx ‖b−Ax‖2 where the matrixA ∈ Cm×n (m ≥ n) has some particular structure arise frequently in applications. Polynomial data fitting is a well-known instance of problems that… Expand

5- PDF

Multiplicative perturbation theory of the Moore–Penrose inverse and the least squares problem☆

- N. Castro-González, F. Dopico, J. M. Molera
- Mathematics
- 15 August 2016

Abstract Bounds for the variation of the Moore–Penrose inverse of general matrices under multiplicative perturbations are presented. Their advantages with respect to classical bounds under additive… Expand

7- PDF

High relative accuracy algorithms for the symmetric eigenproblem

- J. M. Molera
- Mathematics
- 21 December 2008

In this talk we will review the basic facts and results in the field of high relative accuracy. We will see which algorithms and for which classes of matrices give high relative accuracy. In… Expand

Multiple LU factorizations of a singular matrix

- F. Dopico, C. Johnson, J. M. Molera
- Mathematics
- 1 November 2006

A singular matrix A may have more than one LU factorizations. In this work the set of all LU factorizations of A is explicitly described when the lower triangular matrix L is nonsingular. To this… Expand

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