Cristina Jordán

One-point Newton-type iterative methods

In this paper, a unified point of view that includes the most of one-point Newton-type iterative methods for solving nonlinear equations is introduced. A simple idea to design iterative methods with quadratic or cubic convergence is also described. This idea is extended to construct one-point iterative methods of order four. In addition, several numerical examples are given to illustrate and compare different known methods and some introduced by using this unifying idea.

Completions of partial P-matrices with acyclic or non-acyclic associated graph

Abstract In this paper we analyze the positive (sign-symmetric) P -matrix completion problem when the pattern of the partial matrix is non-symmetric. We prove that every positive (sign-symmetric) partial P -matrix A has a positive (sign-symmetric) P -matrix completion when the associated graph of the specified entries of A , G A , is acyclic and we study special cases when G A is not acyclic.

An iterative algorithm for the management of an electric car rental service

The management of a car-rental service becomes more complex as long as one-way bookings between different depots are accepted. These bookings can increase the operational costs due to the necessity of moving vehicles from one depot to another by the company staff in order to attend previously accepted bookings. We present an iterative model based on flows on networks for the acceptance of bookings by a car-rental service that permits one-way reservations. Our model lets us also recover the movement of the fleet of vehicles between the depots over the time. In addition, it also permits including restrictions on the amount of cars managed at every single depot. These results can be of interest for an electric car-rental service that operates at different depots within a city or region.

Inverse M-matrix completion problem with zeros in the inverse completion

In this paper, we obtain an inverse M-matrix completion, with zeros in the inverse completion, of a noncombinatorially symmetric partial inverse M-matrix, when the associated graph is acyclic without specified paths or, in the other case, when the subgraph induced by the vertices of any cycle or specified path is a clique.

Controllability completion problems of partial upper triangular matrices

The main result of this paper states sufficient conditions for the existence of a completion Ac of an n × n partial upper triangular matrix A, such that the pair (Ac B) has prescribed controllability indices, being B an n×m matrix. If A is a partial Hessenberg matrix some conditions may be dropped. An algorithm that obtains a completion Ac of A such that pair (Ac ek ) is completely controllable, where ek is a unit vector, is used to proof the results.

An algorithm for nilpotent completions of partial Jordan matrices

Abstract An algorithm to obtain a completion of a partial upper triangular matrices with prescribed eigenvalues and their multiplicities, and the Jordan chains of the completed matrix is introduced. This algorithm extends some results of Rodman and Shalom in Linear Algebra and Appl. 168 (1992) 221–249.

On the Rodman-Shalom conjecture regarding the Jordan form of completions of partial upper triangular matrices

Dedicated to Hans Schneider on the occasion of his seventieth birthday.jecture the following statement: Let A be a lower irreducible partial upper triangular n n matrix over F such that traceA = 0. L e t n 1 n 2 np 1 be a set of p positive i n tegers such that p X i=1 n i = n. There exists a nilpotent completion Ac of A whose Jordan form consists of p blocks of In this paper this conjecture is solved in two cases: when the minimal rank of A is 2, and for matrices of size 5 5.

On the jordan form of completions of partial upper triangular matrices

Abstract Rodman and Shalom present in Linear Algebra Appl. 168:221–249 (1992) two completion conjectures for partial upper triangular matrices. In this paper we show that one of them is not true in general, and we prove its validity for some particular cases. We also prove the equivalence between the two conjectures in the case of partial Hessenberg matrices.

Highly efficient iterative algorithms for solving nonlinear systems with arbitrary order of convergence p+3, p≥5

Abstract It is known that the concept of optimality is not defined for multidimensional iterative methods for solving nonlinear systems of equations. However, usually optimal fourth-order schemes (extended to the case of several variables) are employed as starting steps in order to design higher order methods for this kind of problems. In this paper, we use a non-optimal (in scalar case) iterative procedure that is specially efficient for solving nonlinear systems, as the initial steps of an eighth-order scheme that improves the computational efficiency indices of the existing methods, as far as the authors know. Moreover, the method can be modified by adding similar steps, increasing the order of convergence three times per step added. This kind of procedures can be used for solving big-sized problems, such as those obtained by applying finite differences for approximating the solution of diffusion problem, heat conduction equations, etc. Numerical comparisons are made with the same existing methods, on standard nonlinear systems and Fisher’s equation by transforming it in a nonlinear system by using finite differences. From these numerical examples, we confirm the theoretical results and show the performance of the proposed schemes.

Smoothing vs. sharpening of color images: Together or separated

Abstract It is still a challenge to improve the efficiency and effectiveness of image denoising and enhancement methods. There exists denoising and enhancement methods that are able to improve visual quality of images. This is usually obtained by removing noise while sharpening details and improving edges contrast. Smoothing refers to the case of denoising when noise follows a Gaussian distribution. Both operations, smoothing noise and sharpening, have an opposite nature. Therefore, there are few approaches that simultaneously respond to both goals. We will review these methods and we will also provide a detailed study of the state-of-the-art methods that attack both problems in colour images, separately.