In this work, the least squares weighted residual method is used to solve the two-dimensional (2D) elasticity problem of a rectangular plate of in-plane dimensions 2a 2b subjected to parabolic edge tensile loads applied at the two edges x = a. The problem is expressed using Beltrami–Michell stress formulation. Airy’s stress function method is applied to the stress compatibility equation, and th...

Abstrucf-Developments in the theory of linear least-squares estimation in the last thirty years or so are outlined. Particular attention is paid to early mathematical. wurk in the field and to more modem developments showing some of the many connections between least-squares filtering and other fields.

Appendix 2B: Proof that the least-squares minimization of a constrained model is equal to the least-squares minimization of an unconstrained model of projected data on the space where the constraint is valid.. Appendix 1: Orthogonality between the column spaces of the matrices in equation [5] 133 6.8.2 Appendix 2: Proof that the least-squares minimization of a constrained model is equal to the ...

Iterative processes for the inversion of structured matrices can be further improved by using a technique for compression and refinement via the least-squares computation. We review such processes and elaborate upon incorporation of this technique into the known frameworks.

We present a series of optimal (in the sense of least-squares) curve fits for the stiffened gas equation of state for single-phase liquid water. At high pressures and (subcritical) temperatures, the parameters produced by these curve fits are found to have very small relative errors: less than 1% in the pressure model, and less than 2% in the temperature model. At low pressures and temperatures...

The Johnson Space Center performed a preliminary reduction of the data taken by a Langley-designed velocity-measuring system using a Hall-eect device during the Crew and Equipment Translation Aid (CETA) experiment on the STS-37 Shuttle ight in April 1991. The data reduction provided average velocity proles. This paper describes a new enhanced data reduction technique based on a least-squares me...

This article deals with estimation of the change-point in a sequence of independent random variables. It is based on a least squares process endowed with a weight function. For finite sample sizes we derive bounds of the error probability. They immediately yield rates of consistency which are known to be optimal. Our findings extend and sharpen earlier results of Antoch, Hušková and Veraverbeke...

Given estimates of the motion eld (optic ow) from an image sequence, it is possible to recover translational direction, ~ T , using a variety of techniques. One such technique, known as \subspace methods," generates constraints which are perpendicular to ~ T , so that two distinct constraints allow a solution for ~ T . In practice many constraints are used in a least-squares solution, but it ha...