We study Newton’s method and method based on linearization for solving quasi-variational inequalities in a finite-dimensional real vector space. Projection methods were the most studied methods for solving quasi-variational inequalities and they have linear rates of the convergence. In the paper we establish sufficient conditions for the convergence of Newton’s method and method of linearizatio...

We show that any regular quadratic matrix polynomial can be reduced to an upper triangular quadratic matrix polynomial over the complex numbers preserving the finite and infinite elementary divisors. We characterize the real quadratic matrix polynomials that are triangularizable over the real numbers and show that those that are not triangularizable are quasi-triangularizable with diagonal bloc...

The present work illustrates the variable viscosity of dust nanofluid runs over a permeable stretched sheet with thermal radiation. The problem has been modelled mathematically introducing the mixed convective condition and magnetic effect. Additionally analysis of entropy generation and Bejan number provides the fine points of the flow. The of model equations are transformed into non-linear or...

In this paper, we have proposed a Haar wavelet quasilinearization method to solve the well known Blasius equation. The method is based on the uniform Haar wavelet operational matrix defined over the interval [0, 1]. In this method, we have proposed the transformation for converting the problem on a fixed computational domain. The Blasius equation arises in the various boundary layer problems of...

In this paper we study the linearizability problem of the two-dimensional complex quasi-cubic system ż = z + (zw)(a30z + a21zw + a12zw + a03w), ẇ = −w − (zw)(b30w + b21wz+b12wz +b03z), where z,w, ai j, bi j ∈ C and d is a real number. We find a transformation to change the quasi-cubic system into an equivalent quintic system and then obtain the necessary and sufficient linearizability condition...

The generalized linear mixed model (GLIMMIX) provides a powerful technique to model correlated outcomes with different types of distributions. The model can now be easily implemented with SAS PROC GLIMMIX in version 9.1. For binary outcomes, linearization methods of penalized quasi-likelihood (PQL) or marginal quasi-likelihood (MQL) provide relatively accurate variance estimates for fixed effec...