In the present paper we propose least squares formulations for the numerical solution of exterior boundary value problems. The partial di erential equation is a rst order system in a bounded subdomain, and the unbounded subdomain is treated by means of boundary integral equations. The rst order system is derived from a strongly elliptic second order system. The analysis of the present least squ...

iv erative methods to solve least squares problems more efficiently. We especially focused on one kind of preconditioners, in which preconditioners are the approximate generalized inverses of the coefficient matrices of the least squares problems. We proposed two different approaches for how to construct the approximate generalized inverses of the coefficient matrices: one is based on the Minim...

This article establishes the asymptotic distributions of generalized method of moments (GMM) estima-tors when the true parameter lies on the boundary of the parameter space. The conditions allow the estimator objective function to be nonsmooth and to depend on preliminary estimators. The boundary of the parameter space may be curved and/or kinked. The article discusses three examples: (1) instr...

We compare four different estimation methods for the coefficients of a linear structural equation with instrumental variables. As the classical methods we consider the limited information maximum likelihood (LIML) estimator and the two-stage least squares (TSLS) estimator, and as the semi-parametric estimation methods we consider the maximum empirical likelihood (MEL) estimator and the generali...

We compare four different estimation methods for a coefficient of a linear structural equation with instrumental variables. As the classical methods we consider the limited information maximum likelihood (LIML) estimator and the two-stage least squares (TSLS) estimator, and as the semi-parametric estimation methods we consider the maximum empirical likelihood (MEL) estimator and the generalized...

The Minimal Residual (MR) is modified for adaptive filtering application. Three forms of MR based algorithm are presented: i) the low complexity SPCG, ii) MREDSI, and iii) MREDSII. The low complexity is a reduced complexity version of a previously proposed SPCG algorithm. Approximations introduced reduce the algorithm to an LMS type algorithm, but, maintain the superior convergence of the SPCG ...

Cauchy’s theorem is used to generate a Complex Variable Boundary Element Method (CVBEM) formulation for steady, two-dimensional potential problems. CVBEM uses the complex potential, w"/#it, to combine the potential function, /, with the stream function, t. The CVBEM formulation, using Cauchy’s theorem, is shown to be mathematically equivalent to Real Variable BEM which employs Green’s second id...