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High order smoothing splines versus least squares problems on Riemannian manifolds

Machado, L.; Leite, F. Silva; Krakowski, K.
Fonte: Centro de Matemática da Universidade de Coimbra Publicador: Centro de Matemática da Universidade de Coimbra
Tipo: Pré-impressão
ENG
Relevância na Pesquisa
76.14%
In this paper, we present a generalization of the classical least squares problem on Euclidean spaces, introduced by Lagrange, to more general Riemannian manifolds. Using the variational definition of Riemannian polynomials, we formulate a high order variational problem on a manifold equipped with a Riemannian metric, which depends on a smoothing parameter and gives rise to what we call smoothing geometric splines. These are curves with a certain degree of smoothness that best fit a given set of points at given instants of time and reduce to Riemannian polynomials when restricted to each subinterval. We show that the Riemannian mean of the given points is achieved as a limiting process of the above. Also, when the Riemannian manifold is an Euclidean space, our approach generates, in the limit, the unique polynomial curve which is the solution of the classical least squares problem. These results support our belief that the approach presented in this paper is the natural generalization of the classical least squares problem to Riemannian manifolds.

Mixture of partial least squares experts and application in prediction settings with multiple operating modes

Souza, Francisco A. A.; Araújo, Rui
Fonte: Elsevier Publicador: Elsevier
Tipo: Artigo de Revista Científica
ENG
Relevância na Pesquisa
66.05%
This paper addresses the problem of online quality prediction in processes with multiple operating modes. The paper proposes a new method called mixture of partial least squares regression (Mix-PLS), where the solution of the mixture of experts regression is performed using the partial least squares (PLS) algorithm. The PLS is used to tune the model experts and the gate parameters. The solution of Mix-PLS is achieved using the expectation–maximization (EM) algorithm, and at each iteration of the EM algorithm the number of latent variables of the PLS for the gate and experts are determined using the Bayesian information criterion. The proposed method shows to be less prone to overfitting with respect to the number of mixture models, when compared to the standard mixture of linear regression experts (MLRE). The Mix-PLS was successfully applied on three real prediction problems. The results were compared with five other regression algorithms. In all the experiments, the proposed method always exhibits the best prediction performance.

Aproximação de Galerkin mínimos-quadrados de escoamentos axissimétricos de fluido Herschel-Bulkley através de expansões abruptas; Galerkin least-squares approximations for herschel bulkley fluid flows through an axisymmetric abrupts expansions

Machado, Fernando Machado
Fonte: Universidade Federal do Rio Grande do Sul Publicador: Universidade Federal do Rio Grande do Sul
Tipo: Dissertação Formato: application/pdf
POR
Relevância na Pesquisa
66.13%
O estudo de escoamentos de fluidos não-Newtonianos através de expansões desperta um grande interesse em pesquisadores nas diversas áreas da engenharia, devido a sua ampla aplicação em indústrias e no meio acadêmico. O objetivo principal desta Dissertação é simular problemas de escoamentos envolvendo fluidos viscoplásticos através de expansões axissimétricas abruptas. O modelo mecânico empregado é baseado nas equações de conservação de massa e de momentum para escoamentos isocóricos acoplados com a equação constitutiva de um Fluido Newtoniano Generalizada (GNL), com a função de viscosidade de Herschel-Bulkley regularizada pela equação de Papanastasiou. O modelo mecânico é aproximado por um modelo estabilizado de elementos finitos, denominado método Galerkin Mínimos-Quadrados, ou Galerkin Least-squares (GLS). Esse método (GLS) é usado a fim superar as dificuldades numéricas do modelo de Galerkin clássico: a condição de Babuška-Brezzi e a instabilidade inerente em regiões advectivas do escoamento. O método é construído adicionando termos de malha-dependentes a fim aumentar a estabilidade da formulação de Galerkin clássica sem danificar sua consistência. A formulação GLS é aplicada para estudar a influência do índice power-law...

Galerkin least-squares solutions for purely viscous flows of shear-thinning fluids and regularized yield stress fluids

Zinani, Flávia Schwarz Franceschini; Frey, Sérgio Luiz
Fonte: Universidade Federal do Rio Grande do Sul Publicador: Universidade Federal do Rio Grande do Sul
Tipo: Artigo de Revista Científica Formato: application/pdf
ENG
Relevância na Pesquisa
66.05%
This paper aims to present Galerkin Least-Squares approximations for flows of Bingham plastic fluids. These fluids are modeled using the Generalized Newtonian Liquid (GNL) constitutive equation. Their viscoplastic behavior is predicted by the viscosity function, which employs the Papanastasiou’s regularization in order to predict a highly viscous behavior when the applied stress lies under the material’s yield stress. The mechanical modeling for this type of flow is based on the conservation equations of mass and momentum, coupled to the GNL constitutive equation for the extra-stress tensor. The finite element methodology concerned herein, the well-known Galerkin Least-Squares (GLS) method, overcomes the two greatest Galerkin shortcomings for mixed problems. There is no need to satisfy Babuška-Brezzi condition for velocity and pressure subspaces, and spurious numerical oscillations, due to the asymmetric nature of advective operator, are eliminated. Some numerical simulations are presented: first, the lid-driven cavity flow of shear-thinning and shear-thickening fluids, for the purpose of code validation; second, the flow of shear-thinning fluids with no yield stress limit, and finally, Bingham plastic creeping flows through 2:1 planar and axisymmetric expansions...

Simulations of incompressible fluid flows by a least squares finite element method

Pereira, V. D.; Campos Silva, J. B.
Fonte: Universidade Estadual Paulista Publicador: Universidade Estadual Paulista
Tipo: Artigo de Revista Científica Formato: 274-282
ENG
Relevância na Pesquisa
66.05%
In this work simulations of incompressible fluid flows have been done by a Least Squares Finite Element Method (LSFEM) using velocity-pressure-vorticity and velocity-pressure-stress formulations, named u-p-ω) and u-p-τ formulations respectively. These formulations are preferred because the resulting equations are partial differential equations of first order, which is convenient for implementation by LSFEM. The main purposes of this work are the numerical computation of laminar, transitional and turbulent fluid flows through the application of large eddy simulation (LES) methodology using the LSFEM. The Navier-Stokes equations in u-p-ω and u-p-τ formulations are filtered and the eddy viscosity model of Smagorinsky is used for modeling the sub-grid-scale stresses. Some benchmark problems are solved for validate the numerical code and the preliminary results are presented and compared with available results from the literature. Copyright © 2005 by ABCM.

A primal-dual interior-point algorithm for nonlinear least squares constrained problems

Costa, M. Fernanda P.; Fernandes, Edite Manuela da G. P.
Fonte: Sociedad Española de Estadística e Investigación Operativa Publicador: Sociedad Española de Estadística e Investigación Operativa
Tipo: Artigo de Revista Científica
Publicado em //2005 ENG
Relevância na Pesquisa
66.16%
This paper extends prior work by the authors on solving nonlinear least squares unconstrained problems using a factorized quasi-Newton technique. With this aim we use a primal-dual interior-point algorithm for nonconvex nonlinear program- ming. The factorized quasi-Newton technique is now applied to the Hessian of the Lagrangian function for the transformed problem which is based on a logarithmic barrier formulation. We emphasize the importance of establishing and maintain- ing symmetric quasi-definiteness of the reduced KKT system. The algorithm then tries to choose a step size that reduces a merit function, and to select a penalty parameter that ensures descent directions along the iterative process. Computa- tional results are included for a variety of least squares constrained problems and preliminary numerical testing indicates that the algorithm is robust and efficient in practice.

Generalized approximating splitting iterations for solving linear least squares problems in finite dimensions

Marti-Lopez,Felipe
Fonte: Sociedade Brasileira de Matemática Aplicada e Computacional Publicador: Sociedade Brasileira de Matemática Aplicada e Computacional
Tipo: Artigo de Revista Científica Formato: text/html
Publicado em 01/08/2005 EN
Relevância na Pesquisa
96.2%
In this paper, a new special class of splitting iterations for solving linear least squares problems in finite dimensions is defined and their main properties of strong global convergence to any problem solution are derived. The investigation results prove the new splitting iterations to be a generalization of the approximating splitting iterations for solving linear least squares problems in finite dimensions, suggesting their suitability for the robust approximate solution of such problems.

Global convergence of a regularized factorized quasi-Newton method for nonlinear least squares problems

Zhou,Weijun; Zhang,Li
Fonte: Sociedade Brasileira de Matemática Aplicada e Computacional Publicador: Sociedade Brasileira de Matemática Aplicada e Computacional
Tipo: Artigo de Revista Científica Formato: text/html
Publicado em 01/06/2010 EN
Relevância na Pesquisa
86.1%
In this paper, we propose a regularized factorized quasi-Newton method with a new Armijo-type line search and prove its global convergence for nonlinear least squares problems. This convergence result is extended to the regularized BFGS and DFP methods for solving strictly convex minimization problems. Some numerical results are presented to show efficiency of the proposed method. Mathematical subject classification: 90C53, 65K05.

A global optimization technique for zero-residual nonlinear least-squares problems

Velazquez Martinez, Leticia
Fonte: Universidade Rice Publicador: Universidade Rice
ENG
Relevância na Pesquisa
66.11%
This thesis introduces a globalization strategy for approximating global minima of zero-residual least-squares problems. This class of nonlinear programming problems arises often in data-fitting applications in the fields of engineering and applied science. Such minimization problems are formulated as a sum of squares of the errors between the calculated and observed values. In a zero-residual problem at a global solution, the calculated values from the model matches exactly the known data. The presence of multiple local minima is the main difficulty. Algorithms tend to get trapped at local solutions when applied to these problems. The proposed algorithm is a combination of a simple random sampling, a Levenberg-Marquardt-type method, a scaling technique, and a unit steplength. The key component of the algorithm is that a unit steplength is used. An interesting consequence is that this approach is not attracted to non-degenerate saddle points or to large-residual local minima. Numerical experiments are conducted on a set of zero-residual problems, and the numerical results show that the new multi-start strategy is relatively more effective and robust than some other global optimization algorithms.

Matrix-Free Polynomial-Based Nonlinear Least Squares Optimized Preconditioning and its Application to Discontinuous Galerkin Discretizations of the Euler Equations

Carr, L.E.; Borges, C.F.; Giraldo, F.X.
Fonte: Escola de Pós-Graduação Naval Publicador: Escola de Pós-Graduação Naval
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
66.09%
Journal of Scientific Computing manuscript; We introduce a preconditioner that can be both constructed and applied using only the ability to apply the underlying operator. Such a preconditioner can be very attractive in scenarios where one has a highly efficient parallel code for applying the operator. Our method constructs a polynomial preconditioner using a nonlinear least squares (NLLS) algorithm. We show that this polynomial-based NLLS-optimized (PBNO) preconditioner significantly improves the performance of a discontinuous Galerkin (DG) compressible Euler equation model when run in an implicit-explicit time integration mode. The PBNO preconditioner achieves significant reduction in GMRES iteration counts and model wall-clock time, and significantly outperforms several existing types of generalized (linear) least squares (GLS) polynomial preconditioners. Comparisons of the ability of the PBNO preconditioner to improve DG model performance when employing the Stabilized Biconjugate Gradient algorithm (BICGS) and the basic Richardson (RICH) iteration are also included. In particular, we show that higher order PBNO preconditioning of the Richardson iteration (run in a dot product free mode) makes the algorithm competitive with GMRES and BICGS in a serial computing environment. Because the NLLS-based algorithm used to construct the PBNO preconditioner can handle both positive definite and complex spectra without any need for algorithm modification...

Indefinite least-squares problems and pseudo-regularity

Giribet, Juan Ignacio; Maestripieri, Alejandra Laura; Martinez Peria, Francisco Dardo
Fonte: Academic Press Inc Elsevier Science Publicador: Academic Press Inc Elsevier Science
Tipo: info:eu-repo/semantics/article; info:ar-repo/semantics/artículo; info:eu-repo/semantics/publishedVersion Formato: application/pdf
ENG
Relevância na Pesquisa
75.99%
The indefinite least-squares problem has been thoroughly studied before under the assumption that the range of C is a uniformly J-positive subspace of K. Along this article the range of C is only supposed to be a J-nonnegative pseudo-regular subspace of K. This work is devoted to present a description for the set of solutions of this abstract problem in terms of the family of J-normal projections onto the range of C.; Fil: Giribet, Juan Ignacio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemáticas; Argentina; Fil: Maestripieri, Alejandra Laura. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemáticas; Argentina; Fil: Martinez Peria, Francisco Dardo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemáticas; Argentina

Accurate solution of structured least squares problems via rank-revealing decompositions

Castro González, Nieves; Ceballos Cañón, Johan Armando; Martínez Dopico, Froilán C.; Molera, Juan M.
Fonte: Society for Industrial and Applied Mathematics Publicador: Society for Industrial and Applied Mathematics
Tipo: info:eu-repo/semantics/publishedVersion; info:eu-repo/semantics/article
Publicado em /07/2013 ENG
Relevância na Pesquisa
96.32%
Least squares problems min(x) parallel to b - Ax parallel to(2) where the matrix A is an element of C-mXn (m >= n) has some particular structure arise frequently in applications. Polynomial data fitting is a well-known instance of problems that yield highly structured matrices, but many other examples exist. Very often, structured matrices have huge condition numbers kappa(2)(A) = parallel to A parallel to(2) parallel to A(dagger)parallel to(2) (A(dagger) is the Moore-Penrose pseudoinverse of A) and therefore standard algorithms fail to compute accurate minimum 2-norm solutions of least squares problems. In this work, we introduce a framework that allows us to compute minimum 2-norm solutions of many classes of structured least squares problems accurately, i.e., with errors parallel to(x) over cap (0) - x(0)parallel to(2)/parallel to x(0)parallel to(2) = O(u), where u is the unit roundoff, independently of the magnitude of kappa(2)(A) for most vectors b. The cost of these accurate computations is O(n(2)m) flops, i.e., roughly the same cost as standard algorithms for least squares problems. The approach in this work relies in computing first an accurate rank-revealing decomposition of A, an idea that has been widely used in recent decades to compute...

Least squares methods in maximum likelihood problems

Osborne, Michael
Fonte: Taylor & Francis Group Publicador: Taylor & Francis Group
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
76.2%
The Gauss-Newton algorithm for solving nonlinear least squares problems proves particularly efficient for solving parameter estimation problems when the number of independent observations is large and the fitted model is appropriate. In this context the c

SDLS: a Matlab package for solving conic least-squares problems

Henrion, Didier; Malick, Jerome
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 17/09/2007
Relevância na Pesquisa
66.16%
This document is an introduction to the Matlab package SDLS (Semi-Definite Least-Squares) for solving least-squares problems over convex symmetric cones. The package is shortly presented through the addressed problem, a sketch of the implemented algorithm, the syntax and calling sequences, a simple numerical example and some more advanced features. The implemented method consists in solving the dual problem with a quasi-Newton algorithm. We note that SDLS is not the most competitive implementation of this algorithm: efficient, robust, commercial implementations are available (contact the authors). Our main goal with this Matlab SDLS package is to provide a simple, user-friendly software for solving and experimenting with semidefinite least-squares problems. Up to our knowledge, no such freeware exists at this date.

OEM for least squares problems

Xiong, Shifeng; Dai, Bin; Qian, Peter Z. G.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
66.26%
We propose an algorithm, called OEM (a.k.a. orthogonalizing EM), intended for var- ious least squares problems. The first step, named active orthogonization, orthogonalizes an arbi- trary regression matrix by elaborately adding more rows. The second step imputes the responses of the new rows. The third step solves the least squares problem of interest for the complete orthog- onal design. The second and third steps have simple closed forms, and iterate until convergence. The algorithm works for ordinary least squares and regularized least squares with the lasso, SCAD, MCP and other penalties. It has several attractive theoretical properties. For the ordinary least squares with a singular regression matrix, an OEM sequence converges to the Moore-Penrose gen- eralized inverse-based least squares estimator. For the SCAD and MCP, an OEM sequence can achieve the oracle property after sufficient iterations for a fixed or diverging number of variables. For ordinary and regularized least squares with various penalties, an OEM sequence converges to a point having grouping coherence for fully aliased regression matrices. Convergence and convergence rate of the algorithm are examined. These convergence rate results show that for the same data set...

A Novel Robust Approach to Least Squares Problems with Bounded Data Uncertainties

Kalantarova, Nargiz; Donmez, Mehmet A.; Kozat, Suleyman S.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 19/03/2012
Relevância na Pesquisa
66.28%
In this correspondence, we introduce a minimax regret criteria to the least squares problems with bounded data uncertainties and solve it using semi-definite programming. We investigate a robust minimax least squares approach that minimizes a worst case difference regret. The regret is defined as the difference between a squared data error and the smallest attainable squared data error of a least squares estimator. We then propose a robust regularized least squares approach to the regularized least squares problem under data uncertainties by using a similar framework. We show that both unstructured and structured robust least squares problems and robust regularized least squares problem can be put in certain semi-definite programming forms. Through several simulations, we demonstrate the merits of the proposed algorithms with respect to the the well-known alternatives in the literature.; Comment: Submitted to the IEEE Transactions on Signal Processing

A Method for Separable Nonlinear Least Squares Problems with Separable Nonlinear Equality Constraints

Kaufman, Linda; Pereyra, Victor
Fonte: Society for Industrial and Applied Mathematics Publicador: Society for Industrial and Applied Mathematics
Tipo: Article; PeerReviewed Formato: application/pdf
Publicado em /02/1978
Relevância na Pesquisa
66.13%
Recently several algorithms have been proposed for solving separable nonlinear least squares problems which use the explicit coupling between the linear and nonlinear variables to define a new nonlinear least squares problem in the nonlinear variables only whose solution is the solution to the original problem. In this paper we extend these techniques to the separable nonlinear least squares problem subject to separable nonlinear equality constraints.

Multilevel First-Order System Least Squares for Nonlinear Elliptic Partial Differential Equations

Codd, Andrea; Manteuffel, T; McCormick, S
Fonte: SIAM Publications Publicador: SIAM Publications
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
66.16%
A fully variational approach is developed for solving nonlinear elliptic equations that enables accurate discretization and fast solution methods. The equations are converted to a first-order system that is then linearized via Newton's method. First-order system least squares (FOSLS) is used to formulate and discretize the Newton step, and the resulting matrix equation is solved using algebraic multigrid (AMG). The approach is coupled with nested iteration to provide an accurate initial guess for finer levels using coarse-level computation. A general theory is developed that confirms the usual full multigrid efficiency: accuracy comparable to the finest-level discretization is achieved at a cost proportional to the number of finest-level degrees of freedom. In a companion paper, the theory is applied to elliptic grid generation (EGG) and supported by numerical results.

Multilevel First-Order System Least Squares for Elliptic Grid Generation

Codd, Andrea; Manteuffel, T; McCormick, S; Ruge, J
Fonte: SIAM Publications Publicador: SIAM Publications
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
66.16%
A new fully variational approach is studied for elliptic grid generation (EGG). It is based on a general algorithm developed in a companion paper [A. L. Codd, T. A. Manteuffel, and S. F. McCormick, SIAM J. Numer. Anal., 41 (2003), pp. 2197-2209] that involves using Newton's method to linearize an appropriate equivalent first-order system, first-order system least squares (FOSLS) to formulate and discretize the Newton step, and algebraic multigrid (AMG) to solve the resulting matrix equation. The approach is coupled with nested iteration to provide an accurate initial guess for finer levels using coarse-level computation. The present paper verifies the assumptions of the companion work and confirms the overall efficiency of the scheme with numerical experiments.

Adaptive algorithm for constrained least-squares problems

Li, Zheng Feng; Osborne, Michael; Prvan, Tania
Fonte: Kluwer Academic Publishers Publicador: Kluwer Academic Publishers
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
66.2%
This paper is concerned with the implementation and testing of an algorithm for solving constrained least-squares problems. The algorithm is an adaptation to the least-squares case of sequential quadratic programming (SQP) trust-region methods for solving general constrained optimization problems. At each iteration, our local quadratic subproblem includes the use of the Gauss-Newton approximation but also encompasses a structured secant approximation along with tests of when to use this approximation. This method has been tested on a selection of standard problems. The results indicate that, for least-squares problems, the approach taken here is a viable alternative to standard general optimization methods such as the Byrd-Omojokun trust-region method and the Powell damped BFGS line search method.