The null space method is a standard method for solving the linear least squares problem subject to equality constraints (the LSE problem). We show that three variants of the method, including one used in LAPACK that is based on the generalized QR factorization, are numerically stable. We derive two perturbation bounds for the LSE problem: one of standard form that is not attainable, and a bound...

Propagation of dust acoustic waves (DAWs) with the effect of power law dust size distribution (DSD) in a magnetized dusty plasma with opposite polarity dust is studied. Using a reductive perturbation method, a Zakharov-Kuznetsov equation appropriate for describing three-dimensional DAWs is derived. The compressive and rarefactive solitons are possible in the present model. Due to the DSD effect...

This paper discusses the application of the perturbation method to handwriting recognition. First the standard pattern recognition operations of preprocessing, feature extraction, and classification are reviewed. Then we introduce the perturbation method as a new approach to overcoming the problems that result from the sequential architecture traditionally found in pattern recognition systems. ...

Hervé Leblond, David Kremer, and Dumitru Mihalache Laboratoire de Photonique d’Angers, Université d’Angers, 2 Bd. Lavoisier, 49045 Angers Cedex 01, France Horia Hulubei National Institute for Physics and Nuclear Engineering (IFIN-HH), 407 Atomistilor, Magurele-Bucharest, 077125, Romania Academy of Romanian Scientists, 54 Splaiul Independentei, Bucharest 050094, Romania Abstract By using a reduc...

A nonlinear Schr\"{o}dinger equation (NLSE) has been derived by employing reductive perturbation method for investigating the modulational instability of dust-ion-acoustic waves (DIAWs) in a four-component plasma having stationary negatively charged dust grains, inertial warm ions, and inertialess non-thermal electrons positrons. It is observed that under consideration, system supports both mod...

The aim of the proposed work is to analyze soliton structures dust-ion acoustic waves obtained in framework Korteg-de Vries (KdV) equation with presence a damping term. concept electron solitary wave an unmagnetized plasma consisting superthermal electrons has been taken into consideration. KdV term derived help reductive perturbation technique and solved by using well-known homotopy analysis m...

an attempt is made for the first time to solve the quadratic and cubic model of magneto hydrodynamic poiseuille flow of phan-thein-tanner (ptt). series solution of magneto hydrodynamic (mhd) flow is developed by using homotopy perturbation method (hpm). results are presented graphically and the effects of non-dimensional parameters on the flow field are analyzed. the results obtained reveals ma...

the present study introduces a new technique of homotopy perturbation method for the solution of systems of fractional partial differential equations. the proposed scheme is based on laplace transform and new homotopy perturbation methods. the fractional derivatives are considered in caputo sense. to illustrate the ability and reliability of the method some examples are provided. the results ob...

The order dependent mapping method, its convergence has recently been proven for the energy eigenvalue of the anharmonic oscillator, is applied to re-sum the standard perturbation series for Stark effect of the hydrogen atom. We perform a numerical experiment up to the fiftieth order of the perturbation expansion. A simple mapping suggested by the analytic structure and the strong field behavio...