Saddle point formulation for gap functions
SADDLE POINT VARIATIONAL METHOD FOR DIRAC CONFINEMENT
... and χ is the Pauli spinor. The free parameter λ which allows deviation from the hydrogen-type and the Gaussian wave functions is taken as fixed during the variational calculation, though it enables us to optimize ...
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Local Fourier analysis for saddle-point problems
... The equations of stationary, incompressible single fluid MHD posed in three dimensions are considered in (for example) [17, 18]. Under some conditions on the data, the existence and uniqueness of solutions to weak ...
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Natural preconditioning and iterative methods for saddle point systems
... all saddle point problems, regardless of the particular ...original saddle point formulation is solvable and, if discretization is required, state an additional condition for the ...
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Preconditioners for the geometry optimisation and saddle point search of molecular systems
... The model “Hessian” of Lindh 12 can be considered as a preconditioner or metric that effects a transformation to a new coordinate system where the optimisation problem is better conditioned, hence algorithms converge ...
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Approximation of the Scattering Amplitude using Nonsymmetric Saddle Point Matrices
... matrix. Functions which are denoted in boldface type typically represent vector valued functions, and real valued functions usually are set in lower case roman or Greek ...
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Saddle Point Approximation to Cumulative Distribution Function for Damage Process
... situations. Saddle point approximations are powered tool in obtaining accurate expressions for distribution functions in closed ...the Saddle point methods to the cumulative ...
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An analysis of low-rank modifications of preconditioners for saddle point systems
... for saddle point systems, subject to low-rank ...The formulation leads to a perturbed hyperbolic quadratic eigen- value ...interior point methods for semidefinite programs, and express the ...
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Nonsmooth Schur-Newton methods for nonsmooth saddle point problems.
... nonlinear Schur complement of (1). Global convergence can be shown by inter- preting it as a descent method for an unconstrained dual problem. In numerical examples the method exhibits mesh independent convergence ...
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Certified reduced basis methods for parametrized saddle point problems
... A detailed review of the reduced basis method, including its historical background and further references, can be found in [83, 95]; here, we shall restrict ourselves to the stages that help us embed this thesis in its ...
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A Saddle-Point Dynamical System Approach for Robust Deep Learning
... inal formulation, we continuously update u corre- sponding to all the images while the w is updated using the gradient information of the loss function evaluated at randomly selected ...
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The antitriangular factorisation of saddle point matrices
... to saddle point ...specific saddle point problems arising in constrained indefinite least squares [16], gives a different but related anti- triangular ...
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Saddle point localization of molecular wavefunctions
... of saddle points and can be intuitively understood based on the classical trajectories shown in ...the saddle point localized trajectories are not eigenstates of the observables x and ...a ...
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The antitriangular factorisation of saddle point matrices
... structures. The antitriangular form of P C makes the equivalence between constraint preconditioners and the nullspace method clear, reveals the eigenvalues of P C −1 A and may provide other insights into the properties ...
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Evaluation of ST preconditioners for saddle point problems
... the saddle point ...the saddle point ...the saddle point problems and to give an estimate of upper bounds for the condition ...
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Null-space preconditioners for saddle point systems
... FOR SADDLE POINT SYSTEMS JENNIFER PESTANA ∗ , TYRONE REES † ...a saddle point system to a smaller, easier to solve, symmetric positive-definite ...
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On the Distribution of a Saddle Point Value in a Random Matrix
... A saddle point is defined as a matrix entry which is the minimal in its row and the maximal in its column, using sharp inequalities, which also imply that at most one could exist in a ...
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Algebraic Multigrid (AMG) for Saddle Point Systems
... To obtain an approximate solution of the PDE, we have to solve a linear system of equations. Direct linear solvers like LU or QR decomposition are not the first choice in this area. Letting N denote the length of the ...
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A Tridiagonalization Method for Symmetric Saddle-Point Systems
... The black dash-dotted curve is the backward error ( 40 ) along lsqr iterations, while the gray curve is the backward error ( 42 ) along the craig iterations. of usymlqr, lsqr and craig b[r] ...
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Refined saddle-point preconditioners for discretized Stokes problems
... elements are very tight. For the stabilized elements a and d overestimate the magni- tude of the extreme eigenvalues, but in almost all cases only by a small amount. The exception is a for Q 1 –Q 1 elements, which is ...
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Combination preconditioning of saddle point systems for positive definiteness
... for saddle point systems, standard iterative methods in nonstandard inner products have been usefully ...preconditioned saddle point matrix nonsymmetric but self-adjoint with respect to a ...
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