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Published **1984**
by National Aeronautics and Space Administration, Langley Research Center in Hampton, Va .

Written in English

- Least squares

**Edition Notes**

Statement | Mohamed M. Hafez, Timothy N. Phillips |

Series | NASA contractor report -- 172372, ICASE report -- no. 84-16 |

Contributions | Phillips, Timothy N, Langley Research Center, Institute for Computer Applications in Science and Engineering |

The Physical Object | |
---|---|

Format | Microform |

Pagination | 1 v. : ill. |

ID Numbers | |

Open Library | OL14928166M |

A MODIFIED LEAST SQUARES FORMULATION FOR A SYSTEM OF FIRST-ORDER EQUATIONS Mohamed M. Hafez* Computer Dynamics, Inc. Timothy N. Phillips Institute for Computer Applications in Science and Engineering Abstract Second-order equations in terms of auxiliary variables similar to potential and stream functions are obtained by applying a weighted least. Second order equations in terms of auxiliary variables similar to potential and stream functions are obtained by applying a weighted least squares formulation to a first order system. The additional boundary conditions which are necessary to solve the higher order equations are determined and numerical results are presented for the Cauchy-Riemann equations. A modified least squares formulation for a system of first-order equations. By M. M. Hafez and T. N. Phillips. Abstract. Second order equations in terms of auxiliary variables similar to potential and stream functions are obtained by applying a weighted least squares formulation to a first order system. The additional boundary conditions which Author: M. M. Hafez and T. N. Phillips. This paper develops a least-squares finite element method for linear elasticity in both two and three dimensions. The least-squares functional is based on the stress-displacement formulation with the symmetry condition of the stress tensor imposed in the first-order system. For the respective displacement and stress, using the Crouzeix--Raviart and Raviart--Thomas finite element spaces, our Cited by:

In this contribution, we propose mixed least‐squares finite element formulations for elastoplastic material behavior. The resulting two‐field formulations depending on displacements and stresses are given through the ‐norm minimization of the residuals of the first‐order system of differential equations. The residuals are the balance of momentum and the constitutive by: 2. In this paper, a first-order system least squares finite element formulation is used to solve the nonlinear system of model equations using different iteration techniques, including an approach. Fully modified least squares (FM-OLS) regression was originally designed in work by Phillips and Hansen () to provide optimal estimates of cointegrating regressions. The method modifies least squares to account for serial correlation effects and for theFile Size: KB. Least Squares Fit (1) The least squares ﬁt is obtained by choosing the α and β so that Xm i=1 r2 i is a minimum. Let ρ = r 2 2 to simplify the notation. Find α and β by minimizing ρ = ρ(α,β). The minimum requires ∂ρ ∂α ˛ ˛ ˛ ˛ β=constant =0 and ∂ρ ∂β ˛ ˛ ˛ ˛ α=constant =0 NMM: Least Squares File Size: KB.

An alternative least-squares formulation of the Navier–Stokes equations with improved mass conservation. formulation of the Navier-Stok es equations first-order system least-squares FEM. () Analysis of First-Order System Least Squares (FOSLS) for Elliptic Problems with Discontinuous Coefficients: Part I. SIAM Journal on Numerical Analysis , Abstract | PDF ( KB)Cited by: The method of least squares is a standard approach in regression analysis to the approximate solution of the over determined systems, in which among the set of equations there are more equations than unknowns. The term “least squares” refers to this situation, the overall solution minimizes the summation of the squares of the errors, which are brought by the results of every single equation. Least Squares Methods for Diﬀerential Equation based Models and Massive Data Sets Josef Kallrath BASF Aktiengesellschaft, GVCS, B, D Ludwigshafen e-mail: [email protected] J 1 Introduction Least squares problems and solution techniques to solve them have a long his-tory brieﬂy addressed by Bj¨orck (, [4]).

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