A variant of the MINRES method, often referred to as the MR-II method, has in the last few years become a popular iterative scheme for computing approximate solutions of large linear discrete ill-posed problems with a symmetric matrix. It is important to terminate the iterations sufficiently early in order to avoid severe amplification of measurement and round-off errors. We present a new L-cur...

This paper explores the potential impacts of introducing real economic incentives in Choice Experiments (CE). While many others have investigated such impacts before, the majority of the literature has focused solely on mitigation of hypothetical bias. We contribute to this literature by widening the scope of research to other behavioural aspects where consumers in CE are often found to deviate...

In this work we develop a method for computing mathematically rigorous enclosures of some one dimensional manifolds of heteroclinic orbits for nonlinear maps. Our method exploits a rigorous curve following argument build on high order Taylor approximation of the local stable/unstable manifolds. The curve following argument is a uniform interval Newton method applied on short line segments. The ...

The article presents the general notions and algorithm about the Gauss-Jordan method. An eloquent example is given and the Turbo C program illustrated this method. We conclude that we can obtain by this method the determinant, by simple calculations and reducing the rounding errors Cuvinte cheie: metoda Gauss-Jordan, matricea inversă, limbaj de programare Turbo C, pivot. 1. Noţiuni generale Met...

Recently developed recursive least squares schemes, where the square root of both the covariance and the information matrix are stored and updated, are known to be particularly suited for parallel implementation. However, when finite precision arithmetic is used, round-off errors apparently accumulate unboundedly, so that after a number of updates the computed least squares solutions turn out t...

This paper describes three numerical methods to collapse a formal product of p pairs of matrices P = Q p?1 k=0 E ?1 k A k down to the product of a single pair ^ E ?1 ^ A. In the setting of linear relations, the product formally extends to the case in which some of the E k 's are singular and it is impossible to explicitly form P as a single matrix. The methods diier in op count, work space, and...

We consider the problem of inferring the probability distribution associated with a language, given data consisting of an infinite sequence of elements of the languge. We do this under two assumptions on the algorithms concerned: (i) like a real-life algorothm it has round-off errors, and (ii) it has no roundoff errors. Assuming (i) we (a) consider a probability mass function of the elements of...

We develop and implement a semi-numerical method for computing high order Taylor approximations of the unstable manifold at a hyperbolic fixed point of a compact infinite dimensional analytic map. Even though the method involves several layers of truncation our goal is to obtain a representation of the invariant manifold which is accurate in a large region about the fixed point. In order to ins...

An iterative algorithm is constructed to solve the generalized coupled Sylvester matrix equations AXB − CYD,EXF − GYH M,N , which includes Sylvester and Lyapunov matrix equations as special cases, over generalized reflexive matrices X and Y . When the matrix equations are consistent, for any initial generalized reflexive matrix pair X1, Y1 , the generalized reflexive solutions can be obtained b...

An important task in solving second order linear ordinary differential equations by the finite difference is to choose a suitable stepsize h. In this paper, by using the stochastic arithmetic, the CESTAC method and the CADNA library we present a procedure to estimate the optimal stepsize hopt, the stepsize which minimizes the global error consisting of truncation and round-off error. Keywords—o...