Decay bounds and algorithms for approximating functions of sparse matrices.
Decomposition of an updated correlation matrix via hyperbolic transformations
An algorithm for hyperbolic singular value decomposition of a given complex matrix based on hyperbolic Householder and Givens transformation matrices is described in detail. The main application of this algorithm is the decomposition of an updated correlation matrix.
Degeneration and complexity of bilinear maps: Some asymptotic spectra.
Determinants of multiplicative Toeplitz matrices
Determination of matrices of the desired 2-D characteristic polynomial
Direct methods for matrix Sylvester and Lyapunov equations.
Discrete-time symmetric polynomial equations with complex coefficients
Discrete-time symmetric polynomial equations with complex coefficients are studied in the scalar and matrix case. New theoretical results are derived and several algorithms are proposed and evaluated. Polynomial reduction algorithms are first described to study theoretical properties of the equations. Sylvester matrix algorithms are then developed to solve numerically the equations. The algorithms are implemented in the Polynomial Toolbox for Matlab.
Efficient computation of enclosures for the exact solvents of a quadratic matrix equation.
Efficient Computing of some Vector Operations over GF(3) and GF(4)
The problem of efficient computing of the affine vector operations (addition of two vectors and multiplication of a vector by a scalar over GF (q)), and also the weight of a given vector, is important for many problems in coding theory, cryptography, VLSI technology etc. In this paper we propose a new way of representing vectors over GF (3) and GF (4) and we describe an efficient performance of these affine operations. Computing weights of binary vectors is also discussed.
Eine Faktorisierung der bei der rationalen Interpolation auftretenden Matrizen.
Enclosures for the solution set of parametric interval linear systems
We investigate parametric interval linear systems of equations. The main result is a generalization of the Bauer-Skeel and the Hansen-Bliek-Rohn bounds for this case, comparing and refinement of both. We show that the latter bounds are not provable better, and that they are also sometimes too pessimistic. The presented form of both methods is suitable for combining them into one to get a more efficient algorithm. Some numerical experiments are carried out to illustrate performances of the methods....
Error analysis of some approximating algorithms
Error Analysis of Splitting Algorithms for Polynomials.
Evaluating matrix functions for exponential integrators via Carathéodory-Fejér approximation and contour integrals.
Evaluating the Frechet derivative of the matrix exponential.
Extension de la méthode Procuste à la comparaison de nuages de points situés dans des espaces de dimensions différentes
Fast Givens Rotations for Orthogonal Similarity Transformations
Fast solution of a certain Riccati equation through Cauchy-like matrices.
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...
Finding nonoverlapping substructures of a sparse matrix.