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Saturday, May 9, 2020 | History

3 edition of A modified least squares formulation for a system of first-order equations found in the catalog.

A modified least squares formulation for a system of first-order equations

M. M Hafez

# A modified least squares formulation for a system of first-order equations

## by M. M Hafez

Written in English

Subjects:
• Least squares

• Edition Notes

The Physical Object ID Numbers 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 Format Microform Pagination 1 v. : ill. Open Library OL14928166M

This linear system has a special name, the normal equations. It is the most direct way of solving a linear least squares problem, and as long as ATAis reasonably well conditioned is a great method. 2You may be uncomfortable with differentiating expressions such as this with respect to . Part IV Least-Squares Finite Element Methods for Other Settings 8 The Navier-Stokes Equations First-Order System Formulations of the Navier-Stokes Equations Least-Squares Principles for the Navier-Stokes Equations Continuous Least-Squares Principles Discrete Least-Squares Principles

These videos follow Chapters of my book "Applied Linear Algebra: The Decoupling Principle", and were made for the corresponding class (M) that I developed at the University of Texas. This is the first book devoted to the least-squares finite element method (LSFEM), which is a simple, efficient and robust technique for the numerical solution of partial differential equations. The book demonstrates that the LSFEM can solve a broad range of problems in fluid dynamics and electromagnetics with only one mathematical Price: \$

in a defined way like other iterative methods, but like direct methods, terminating with the exact solution after at most n steps, at least in theory. Many expectations were disappointed, when it was found out that due to roundoff the n-step termination property does not hold in r, viewed as an iterative method, the cg-algorithm has very attractive by: Based on Least-Squares and Modiﬁed Variational Principles Pavel Bochev1 University of Texas at Arlington Department of mathematics [email protected] Ap 1This work is partially supported by Com2MaC-KOSEF and the National Sci-ence Foundation under grant number DMS

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### A modified least squares formulation for a system of first-order equations by M. M Hafez Download PDF EPUB FB2

A modified least squares formulation for a system of first-order equations. Get this from a library. A modified least squares formulation for a system of first-order equations.

[M M Hafez; Timothy N Phillips; Langley Research Center.; Institute for Computer Applications in Science and Engineering.]. 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. Hafez and T. 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. Hafez and T. 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 AnalysisAbstract | 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 (, ).

In this paper, we study the least-squares finite element methods (LSFEM) for the linear hyperbolic transport equations. The linear transport equation naturally allows discontinuous solutions and discontinuous inflow conditions, while the normal component of the flux across the mesh faces needs to.

M Hafez has written: 'A modified least squares formulation for a system of first-order equations' -- subject(s): Least squares Asked in Math and Arithmetic, Algebra, Geometry What makes 2. the sum in order to satisfy the DEs as well as possible (e.g., by least-squares).

Additionally, in spectral methods, the constraints must then be enforced. This is done by replacing one (or more) of the least-squares equations with the constraint conditions. The proposed method proceeds in Cited by: Second-order Least Squares Estimation in Nonlinear Models Liqun Wang Department of Statistics University of Manitoba e-mail: [email protected] File Size: KB.

3 The Method of Least Squares 4 1 Description of the Problem Often in the real world one expects to ﬁnd linear relationships between variables.

For example, the force of a spring linearly depends on the displacement of the spring: y = kx (here y is the force, x is the displacement of the spring from rest, and k is the spring constant).

To test. The modified Navier-Stokes equations are expressed as an equivalent set of first-order equations by introducing vorticity-dilatation or stresses as additional independent variables and the least-squares method is used to develop the finite element model.

High. Non-linear least squares is the form of least squares analysis used to fit a set of m observations with a model that is non-linear in n unknown parameters (m ≥ n). It is used in some forms of nonlinear regression. The basis of the method is to approximate the model by a linear one and to refine the parameters by successive iterations.M.

M Hafez has written: 'A modified least squares formulation for a system of first-order equations' -- subject(s): Least squares Asked in Factoring and Multiples Each composite number has a least.Here, in this article, we introduce a least-squares-based weak Galerkin finite element method for the second order elliptic equation.

This new method is shown to provide very accurate numerical approximations for both the primal and the flux variables. In contrast to other existing least-squares.