K e y w o r d s O b s t a c l e problem, Multilevel projection, Convergence, Finite element, Error estimate. 1 . I N T R O D U C T I O N The obstacle problem we consider here can be described as follows: find the equilibrium position u = u(x), x E f~ C R 2 of an elastic membrane constrained to lie above a given obstacle @ = @(x) under an external force f (x ) . Then u(x) is the formal solution ...

We propose a modification of the classical proximal point algorithm for finding zeroes of a maximal monotone operator in a Hilbert space. In particular, an approximate proximal point iteration is used to construct a hyperplane which strictly separates the current iterate from the solution set of the problem. This step is then followed by a projection of the current iterate onto the separating h...

Denoising is the problem of removing the inherent noise from an image. The standard noise model is additive white Gaussian noise, where the observed image f is related to the underlying true image u by the degradation model f = u+ η, and η is supposed to be at each pixel independently and identically distributed as a zero-mean Gaussian random variable. Since this is an ill-posed problem, Rudin,...

Motif finding is one of the NP-complete problems in Computational Biology. Existing nondeterministic algorithms for motif finding do not guarantee the global optimality of results and are sensitive to initial parameters. To address this problem, the PROJECTION algorithm provides a good initial estimate that can be further refined using local optimization algorithms such as EM, MEME or Gibbs. Fo...

We derive a new adaptive filtering algorithm called the Instrumental Variable Affine Projection (IVAP) algorithm and give its fast version (FIVAP algorithm). The IVAP algorithm departs from the AP algorithm and uses an IV. The IV process is generated in a way such that the new algorithm combines between the AP and the Fast Newton Transversal Filter (FNTF) algorithms. Simulations show that the I...

The paper deals with the stability of control algorithms in extended operational space for redundant robots. We compare the performance of the control algorithm based on minimal-null space projection and pseudoinverse based projection into the Jacobian null space. We show how the null-space projection affects the stability of the null-space tracking algorithm. The results are verified with the ...