Regularization of nonlinear ill-posed equations with accretive operators.
Regularized nonnegative matrix factorization: geometrical interpretation and application to spectral unmixing
Regulatory network of drug-induced enzyme production: parameter estimation based on the periodic dosing response measurement
The common goal of systems pharmacology, i.e. systems biology applied to the field of pharmacology, is to rely less on trial and error in designing an input-output systems, e.g. therapeutic schedules. In this paper we present, on the paradigmatic example of a regulatory network of drug-induced enzyme production, the further development of the study published by Duintjer Tebbens et al. (2019) in the Applications of Mathematics. Here, the key feature is that the nonlinear model in form of an ODE system...
Rehabilitation of the Gauss-Jordan Algorithm.
Relations Between Condition Numbers and the Convergence of the Jacobi Method for Real Positive Definite Matrices.
Relative bilinear complexity and matrix multiplication.
Relaxation bei komplexen Matrizen.
Relaxation bei nichtsymmetrischen Matrizen.
Remarks on inertia theorems for matrices
Remarks on polynomial methods for solving systems of linear algebraic equations
For a large system of linear algebraic equations , the approximate solution is computed as the -th order Fourier development of the function , related to orthogonal polynomials in space. The domain in the complex plane is assumed to be known. This domain contains the spectrum of the matrix . Two algorithms for are discussed. Two possibilities of preconditioning by an application of the so called Richardson iteration process with a constant relaxation coefficient are proposed. The case...
Remarks on restriction eigenfunctions in .
Remarques sur la convergence de la méthode Q.R.
Remarques sur les algorithmes de décomposition de domaines
Reorthoganization in the block Lanczos algorithm
Replicant compression coding in Besov spaces
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 on a regular domain of 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
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 on a regular domain of The result is: if then the Kolmogorov metric entropy satisfies . This...
Řešení soustav lineárních algebraických rovnic s komplexními koeficienty
Residual norm behavior for Hybrid LSQR regularization
Hybrid LSQR represents a powerful method for regularization of large-scale discrete inverse problems, where ill-conditioning of the model matrix and ill-posedness of the problem make the solutions seriously sensitive to the unknown noise in the data. Hybrid LSQR combines the iterative Golub-Kahan bidiagonalization with the Tikhonov regularization of the projected problem. While the behavior of the residual norm for the pure LSQR is well understood and can be used to construct a stopping criterion,...
Resilient asynchronous primal Schur method
This paper introduces the application of asynchronous iterations theory within the framework of the primal Schur domain decomposition method. A suitable relaxation scheme is designed, whose asynchronous convergence is established under classical spectral radius conditions. For the usual case where local Schur complement matrices are not constructed, suitable splittings based only on explicitly generated matrices are provided. Numerical experiments are conducted on a supercomputer for both Poisson's...
Résolution de grands systèmes linéaires creux par méthodes itératives parallèles