A method for stable numerical differentiation of noisy data is proposed. The method requires solving a Volterra integral equation of the second kind. This equation is solved analytically. In the examples considered its solution is computed analytically. Some numerical results of its application are presented. These examples show that the proposed method for stable numerical differentiation is n...

A standard way to solve linear algebraic systems Au = f, (*) with ill-conditioned matrices A is to use variational regularization. This leads to solving the equation (A * A + aI)u = A * f δ , where a is a regularization parameter, and f δ are noisy data, ||f − f δ || ≤ δ. Numerically it requires to calculate products of matrices A * A and inversion of the matrix A * A + aI which is also ill-con...

in this paper a new form of the homptopy perturbation method is used for solving oscillator differential equation, which yields the maclaurin series of the exact solution. nonlinear vibration problems and differential equation oscillations have crucial importance in all areas of science and engineering. these equations equip a significant mathematical model for dynamical systems. the accuracy o...

In this paper, an iterative method is proposed for solving matrix equation $sum_{j=1}^s A_jX_jB_j = E$. This method is based on the global least squares (GL-LSQR) method for solving the linear system of equations with the multiple right hand sides. For applying the GL-LSQR algorithm to solve the above matrix equation, a new linear operator, its adjoint and a new inner product are dened. It is p...

in this paper, an iterative method is proposed for solving large general sylvester matrix equation $axb+cxd = e$, where $a in r^{ntimes n}$ , $c in r^{ntimes n}$ , $b in r^{stimes s}$ and  $d in r^{stimes s}$ are given matrices and $x in r^{stimes s}$  is the unknown matrix. we present a global conjugate gradient (gl-cg) algo- rithm for solving linear system of equations with multiple right-han...

in this paper, an iterative method is proposed for solving matrix equation $sum_{j=1}^s a_jx_jb_j = e$. this method is based on the global least squares (gl-lsqr) method for solving the linear system of equations with the multiple right hand sides. for applying the gl-lsqr algorithm to solve the above matrix equation, a new linear operator, its adjoint and a new inner product are dened. it is ...

Phase unwrapping for a noisy image suffers from many singular points. Singularity-spreading methods are useful for the noisy image to regularize the singularity. However, the methods have a drawback of distorting phase distribution in a regular area that contains no singular points. When the singular points are confined in some local areas, the regular region is not distorted. This paper propos...

this paper presents a computational method for solving two types of integro-differential equations, system of nonlinear high order volterra-fredholm integro-differential equation(vfides) and nonlinear fractional order integro-differential equations. our tools for this aims is operational matrices of integration and fractional integration. by this method the given problems reduce to solve a syst...

In this paper we use equation solving for translating internal tests derived for a component embedded within a composite system into external tests defined over the external alphabets of the system. The composite system is represented as two communicating finite state machines (FSMs), an embedded component FSM, and a context FSM that models the remaining part of the system and which is assumed ...

blind source separation technique separates mixed signals blindly without any information on the mixing system. in this paper, we have used two evolutionary algorithms, namely, genetic algorithm and particle swarm optimization for blind source separation. in these techniques a novel fitness function that is based on the mutual information and high order statistics is proposed. in order to evalu...