This paper is concerned with the computation of accurate approximate solutions of linear systems of equations and linear least-squares problems with a very ill-conditioned matrix and error-contaminated data. The solution of this kind of problems requires regularization. Common regularization methods include the truncated singular value decomposition and truncated iteration with a Krylov subspac...

The various industrial and engineering applications of flow of fluid between parallel plates have continued to generate renewed interests. In this work, a comparative study of approximate analytical methods is carried out using differential transformation,homotopy perturbation, Adomian decomposition, variation of parameter and variational iteration methods for the analysis of a steady two-dimen...

We propose to speed up the training process of support vector machines (SVM) by resorting to an approximate SVM, where a small number of representatives are extracted from the original training data set and used for training. Theoretical studies show that, in order for the approximate SVM to be similar to the exact SVM given by the original training data set, kernel k-means should be used to ex...

The HAPPYNET problem is defined as follows : Given a undirected simple graph G with integer weights wvu on its edges vu ∈ E(G), find a function s : V (G) −→ {−1, 1} such that ∀v ∈ V (G), v is happy in G, i.e. such that u∈Γ(v) s(v)s(u)wuv ≥ 0. It is easy to see that HAPPYNET has always a solution, no matter what the input is. However, no polynomial algorithm is known for this problem, which is c...

In earlier papers we have developed an algebraic theory of discrete tomography. In those papers the structure of the functions f : A → {0, 1} and f : A → Z having given line sums in certain directions have been analyzed. Here A was a block in Z with sides parallel to the axes. In the present paper we assume that there is noise in the measurements and (only) that A is an arbitrary or convex fini...

and Applied Analysis 3 Proof. As T and S form a K-Cyclic map, d x1, x2 d Tx0, Sx1 ≤ k d x0, Tx0 d x1, Sx1 1 − 2k d A,B k d x0, x1 d x1, x2 1 − 2k d A,B . 3.1 So, it follows that d x1, x2 ≤ k/ 1 − k d x0, x1 1 − k/ 1 − k d A,B . Similarly, it can be seen that d x2, x3 ≤ ( k 1 − k )2 d x0, x1 [ 1 − ( k 1 − k )2] d A,B . 3.2 Hence, it follows by induction that d xn, xn 1 ≤ ( k 1 − k )n d x0, x1 [ ...

Doubly periodic solutions for the Lagrange{Euler equation of the (1+1)-dimensional scalar ' 4 theory are studied. Provided that nonlin-ear term is small, the Poincare{Lindstedt asymptotic method is used to nd asymptotic solutions in the standing wave form. It is proved that using the Jacobi elliptic function cn as a zero approximation one can solve the problem of the main resonance, appearing i...

We propose a new approximate method for counting the number of the solutions for constraint satisfaction problem (CSP). The method derives from the partition function based on introducing the free energy and capturing the relationship of probabilities of variables and constraints, which requires the marginal probabilities. It firstly obtains the marginal probabilities using the belief propagati...

The spline collocation method is used to approximate solutions of boundary value problems. The convergence analysis is given and the method is shown to have second-order convergence. A numerical illustration is given to show the pertinent features of the technique.  

The problem of positioning p points so as to maximize the minimum distance between them has been studied in both location theory (as the continuous p-dispersion problem) and the design of computer experiments (as the maximin distance design problem). This problem can be formulated as a nonlinear program, either exactly or approximately. We consider formulations of both types and demonstrate tha...