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A leastsquares approach based on a discrete minus one inner product for first order systems
 MATH. COMP
, 1997
"... The purpose of this paper is to develop and analyze a leastsquares approximation to a first order system. The first order system represents a reformulation of a second order elliptic boundary value problem which may be indefinite and/or nonsymmetric. The approach taken here is novel in that the le ..."
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Cited by 86 (12 self)
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in that the leastsquares functional employed involves a discrete inner product which is related to the inner product in H −1 (Ω) (the Sobolev space of order minus one on Ω). The use of this inner product results in a method of approximation which is optimal with respect to the required regularity as well
LeastSquares Methods For Linear Elasticity Based On A Discrete Minus One Inner Product
, 2001
"... The purpose of this paper is to develop and analyze leastsquares approximations for elasticity problems. The major advantage of the leastsquare formulation is that it does not require that the classical LadyzhenskayaBabuskaBrezzi (LBB) condition be satised. By employing leastsquares functionals ..."
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Cited by 8 (3 self)
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functionals which involve a discrete inner product which is related to the inner product in H 1(
FirstOrder System LeastSquares For The Helmholtz Equation
, 2000
"... This paper develops a multilevel leastsquares approach for the numerical solution of the complex scalar exterior Helmholtz equation. This secondorder equation is first recast into an equivalent firstorder system by introducing several "field" variables. A combination of scaled L 2 and ..."
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Cited by 15 (0 self)
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This paper develops a multilevel leastsquares approach for the numerical solution of the complex scalar exterior Helmholtz equation. This secondorder equation is first recast into an equivalent firstorder system by introducing several "field" variables. A combination of scaled L 2
LEASTSQUARES METHODS FOR COMPUTATIONAL
, 2004
"... Major Subject: Mathematics iii Leastsquares Methods for Computational Electromagnetics. (August 2004) ..."
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Major Subject: Mathematics iii Leastsquares Methods for Computational Electromagnetics. (August 2004)
FIRSTORDER SYSTEM LEASTSQUARES FOR THE OSEEN EQUATIONS
"... Abstract. Following earlier work for Stokes equations, a leastsquares functional is developed for two and threedimensional Oseen equations. By introducing a velocity flux variable and associated curl and trace equations, ellipticity is established in an appropriate product norm. The form of Oseen ..."
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Abstract. Following earlier work for Stokes equations, a leastsquares functional is developed for two and threedimensional Oseen equations. By introducing a velocity flux variable and associated curl and trace equations, ellipticity is established in an appropriate product norm. The form
LeastSquares Method
, 2009
"... A highorder Galerkin LeastSquares (GLS) finite element discretization is combined with massively parallel implicit solvers. The stabilization parameter of the GLS discretization is modified to improve the resolution characteristics and the condition number for the highorder interpolation. The Bal ..."
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A highorder Galerkin LeastSquares (GLS) finite element discretization is combined with massively parallel implicit solvers. The stabilization parameter of the GLS discretization is modified to improve the resolution characteristics and the condition number for the highorder interpolation
Leastsquares Problems
"... The multilinear leastsquares (MLLS) problem is an extension of the linear leastsquares problem. The difference is that a multilinear operator is used in place of a matrixvector product. The MLLS is typically a largescale problem characterized by a large number of local minimizers. It originates, ..."
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The multilinear leastsquares (MLLS) problem is an extension of the linear leastsquares problem. The difference is that a multilinear operator is used in place of a matrixvector product. The MLLS is typically a largescale problem characterized by a large number of local minimizers. It originates
Regularized LeastSquares Classification
"... We consider the solution of binary classification problems via Tikhonov regularization in a Reproducing Kernel Hilbert Space using the square loss, and denote the resulting algorithm Regularized LeastSquares Classification (RLSC). We sketch ..."
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Cited by 100 (1 self)
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We consider the solution of binary classification problems via Tikhonov regularization in a Reproducing Kernel Hilbert Space using the square loss, and denote the resulting algorithm Regularized LeastSquares Classification (RLSC). We sketch
LeastSquares for Second Order Elliptic Problems
 Comput. Meth. Appl. Mech. Engrg
, 1997
"... In this paper, we introduce and analyze two leastsquares methods for second order elliptic differential equations with mixed boundary conditions. These methods extend to problems which involve oblique derivative boundary conditions as well as nonsymmetric and indefinite problems as long as the orig ..."
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Cited by 10 (3 self)
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size h) and will be shown to converge at an optimal rate. The first leastsquares method involves a discrete, computable H \Gamma1 norm of the residual and stabilization terms consisting of the jumps at the interelement boundaries and a weighted elementwise L 2 norm of the residual over the finite
Results 1  10
of
2,695,659