On a Theorem of Stein-Rosenberg Type in Interval Analysis.
On an algorithm for testing T4 solvability of max-plus interval systems
In this paper, we shall deal with the solvability of interval systems of linear equations in max-plus algebra. Max-plus algebra is an algebraic structure in which classical addition and multiplication are replaced by and , where , . The notation represents an interval system of linear equations, where and are given interval matrix and interval vector, respectively. We can define several types of solvability of interval systems. In this paper, we define the T4 solvability and give an algorithm...
On continuous interval functions
On convergence of Börsch-Supan's method with Weierstrass' corrections.
On error estimation in the conjugate gradient method and why it works in finite precision computations.
On exact solutions of a class of interval boundary value problems
In this article, we deal with the Boundary Value Problem (BVP) for linear ordinary differential equations, the coefficients and the boundary values of which are constant intervals. To solve this kind of interval BVP, we implement an approach that differs from commonly used ones. With this approach, the interval BVP is interpreted as a family of classical (real) BVPs. The set (bunch) of solutions of all these real BVPs we define to be the solution of the interval BVP. Therefore, the novelty of the...
On Newton-like methods to enclose solutions of nonlinear equations
We present a class of Newton-like methods to enclose solutions of systems of nonlinear equations. Theorems are derived concerning the feasibility of the method, its global convergence, its speed and the quality of enclosure.
On Optimal Global Error Bounds Obtained by Scaled Local Error Estimates.
On sums of dependent uniformly distributed random variables.
We study and solve several functional equations which yield necessary and sufficient conditions for the sum of two uniformly distributed random variables to be uniformly distributed.
On the Arithmetic of Errors
An approximate number is an ordered pair consisting of a (real) number and an error bound, briefly error, which is a (real) non-negative number. To compute with approximate numbers the arithmetic operations on errors should be well-known. To model computations with errors one should suitably define and study arithmetic operations and order relations over the set of non-negative numbers. In this work we discuss the algebraic properties of non-negative numbers starting from familiar properties of...
On the Convergence of Powers of Interval Matrices (2).
On the Convergence Order of Accelerated Root Iterations.
On the convergence rate of the conjugate gradients in presence of rounding errors.
On the Distribution of Errors in the Iterative Solution of a System of Linear Equations. II..
On the Distribution of Errors in the Iterative Solution of a System of Linear Equations.
On the gap between the semilocal convergence domains of two Newton methods
We answer a question posed by Cianciaruso and De Pascale: What is the exact size of the gap between the semilocal convergence domains of the Newton and the modified Newton method? In particular, is it possible to close it? Our answer is yes in some cases. Using some ideas of ours and more precise error estimates we provide a semilocal convergence analysis for both methods with the following advantages over earlier approaches: weaker hypotheses; finer error bounds on the distances involved, and at...
On the improved family of simultaneous methods for the inclusion of multiple polynomial zeros.
On the iterative inclusion of solutions in initial value problems
On the minimum error in addition processes of positive floating-point numbers
On the Numerical Solution of the Equation ....-(....) = f and Its Discretizations, I.