We initiate the complexity theoretic study of the problem of computing the bits of (real) algebraic numbers. This extends the work of Yap on computing the bits of transcendental numbers like π, in Logspace. Our main result is that computing a bit of a fixed real algebraic number is in C=NC 1⊆ L when the bit position has a verbose (unary) representation and in the counting hierarchy when it has ...

Communicated by [editor] In this paper we use the Gröbner representation of a binary linear code C to give efficient algorithms for computing the whole set of coset leaders, denoted by CL(C) and the set of leader codewords, denoted by L(C). The first algorithm could be adapted to provide not only the Newton and the covering radius of C but also to determine the coset leader weight distribution....

PDE-constrained optimization problems, and the development of preconditioned iterative methods for the efficient solution of the arising matrix system, is a field of numerical analysis that has recently been attracting much attention. In this paper, we analyze and develop preconditioners for matrix systems that arise from the optimal control of reaction-diffusion equations, which themselves res...

We determine the L p-L q-estimate of the linear equations of thermoelasticity for rhom-bic media in R 2. For this purpose we will transform the equations to an evolution equation showing that this equation has a unique solution with the help of the semigroup theory. In order to obtain the L p-L q-estimate, we will first apply the Fourier transformation to the evolution equation, thus determinin...

Data Flow is a natural paradigm representing distributed programs able to express data and control dependencies between composing nodes. Our work concentrates on periodic Data-Flow programs having Hard Real-Time constraints. We propose a model and a string-based representation for a relevant class of Data-Flow programs and present a two-phase algorithm able to compute a schedule for a given set...

The main idea in object tracking is to support the processing of incoming images by predicting future object’s poses and features using the knowledge about the object’s previous motion. In this paper we present a new method for the prediction and adjustment of motion parameters to the current measurements using the quaternion representation for the orientation and the Gauss-Newton iteration on ...

Lagrange interpolation by polynomials in several variables is studied through a finite difference approach. We establish an interpolation formula analogous to that of Newton and a remainder formula, both of them in terms of finite differences. We prove that the finite difference admits an integral representation involving simplex spline functions. In particular, this provides a remainder formul...

This work concerns the optimal regulation of single-input-single-output nonminimum-phase nonlinear processes of relative order one. The problem of calculation of an ISE-optimal, statically equivalent, minimum-phase output for nonminimum-phase compensation is formulated using Hamilton-Jacobi theory and the normal form representation of the nonlinear system. A Newton-Kantorovich iteration is deve...