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744,979
QuasiNewton Methods With Derivatives
, 1995
"... When the Jacobian of a nonlinear system of equations is fully available, the main drawback for the application of Newton's method is the linear algebra work associated with its basic iteration. In many cases, quasiNewton methods "with cheap linear algebra" can be applied. The availa ..."
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When the Jacobian of a nonlinear system of equations is fully available, the main drawback for the application of Newton's method is the linear algebra work associated with its basic iteration. In many cases, quasiNewton methods "with cheap linear algebra" can be applied
Variational Problems in Quasi–Newton Methods
, 2006
"... It has been known since the early 1970s that the Hessian matrices in quasi– Newton methods can be updated by variational means, in several different ways. The usual formulation of these variational problems uses a coordinate system, and the symmetry of the Hessian matrices are enforced as explicit c ..."
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quasi–Newton methods in the future. Key words. Quasi–Newton, DFP, BFGS, variational problems, duality, sparse problems.
Variational Problems in Quasi–Newton Methods
, 2006
"... It has been known since the early 1970s that the Hessian matrices in quasi– Newton methods can be updated by variational means, in several different ways. The usual formulation of these variational problems uses a coordinate system, and the symmetry of the Hessian matrices are enforced as explicit c ..."
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new quasi–Newton methods in the future. Key words. Quasi–Newton, DFP, BFGS, variational problems, duality, sparse problems.
Immersed Interface Methods For Stokes Flow With Elastic Boundaries Or Surface Tension
 SIAM J. Sci. Comput
"... . A second order accurate interface tracking method for the solution of incompressible Stokes flow problems with moving interfaces on a uniform Cartesian grid is presented. The interface may consist of an elastic boundary immersed in the fluid or an interface between two different fluids. The interf ..."
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Cited by 117 (14 self)
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(SIAM J. Numer. Anal., 31(1994), pp. 10191044). The resulting velocities are interpolated to the interface to determine the motion of the interface. An implicit quasiNewton method is developed that allows reasonable time steps to be used. Key words. Stokes flow, creeping flow, interface tracking
Implicit Fairing of Irregular Meshes using Diffusion and Curvature Flow
, 1999
"... In this paper, we develop methods to rapidly remove rough features from irregularly triangulated data intended to portray a smooth surface. The main task is to remove undesirable noise and uneven edges while retaining desirable geometric features. The problem arises mainly when creating highfidelit ..."
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Cited by 540 (23 self)
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fidelity computer graphics objects using imperfectlymeasured data from the real world. Our approach contains three novel features: an implicit integration method to achieve efficiency, stability, and large timesteps; a scaledependent Laplacian operator to improve the diffusion process; and finally, a robust
QuasiNewton methods on Grassmannians and multilinear approximations of tensors
, 2009
"... Abstract. In this paper we proposed quasiNewton and limited memory quasiNewton methods for objective functions defined on Grassmann manifolds or a product of Grassmann manifolds. Specifically we defined bfgs and lbfgs updates in local and global coordinates on Grassmann manifolds or a product of ..."
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Cited by 17 (3 self)
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Abstract. In this paper we proposed quasiNewton and limited memory quasiNewton methods for objective functions defined on Grassmann manifolds or a product of Grassmann manifolds. Specifically we defined bfgs and lbfgs updates in local and global coordinates on Grassmann manifolds or a product
Efficient and Effective Clustering Methods for Spatial Data Mining
, 1994
"... Spatial data mining is the discovery of interesting relationships and characteristics that may exist implicitly in spatial databases. In this paper, we explore whether clustering methods have a role to play in spatial data mining. To this end, we develop a new clustering method called CLARANS which ..."
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Cited by 700 (37 self)
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Spatial data mining is the discovery of interesting relationships and characteristics that may exist implicitly in spatial databases. In this paper, we explore whether clustering methods have a role to play in spatial data mining. To this end, we develop a new clustering method called CLARANS which
New Implicit Updates in Multistep QuasiNewton Methods for Unconstrained Optimisation
 Comput. Math. Appl
, 2001
"... Multistep quasiNewton methods for optimisation (using data from more than one previous step to revise the current approximate Hessian) were introduced by Ford and Moghrabi in [4], where they showed how to construct such methods by means of interpolating curves. These methods also utilise standard ..."
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Cited by 4 (2 self)
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Multistep quasiNewton methods for optimisation (using data from more than one previous step to revise the current approximate Hessian) were introduced by Ford and Moghrabi in [4], where they showed how to construct such methods by means of interpolating curves. These methods also utilise standard
QuasiNewton methods – A new direction
 In Proceedings of the 29th Annual International Conference on Machine Learning
, 2012
"... Four decades after their invention, quasiNewton methods are still state of the art in unconstrained numerical optimization. Although not usually interpreted thus, these are learning algorithms that fit a local quadratic approximation to the objective function. We show that many, including the most ..."
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Cited by 9 (1 self)
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Four decades after their invention, quasiNewton methods are still state of the art in unconstrained numerical optimization. Although not usually interpreted thus, these are learning algorithms that fit a local quadratic approximation to the objective function. We show that many, including the most
Hybrid RungeKutta and QuasiNewton Methods for unconstrained . . .
, 2011
"... Finding a local minimizer in unconstrained nonlinear optimization and a fixed point of a gradient system of ordinary differential equations (ODEs) are two closely related problems. QuasiNewton algorithms are widely used in unconstrained nonlinear optimization while RungeKutta methods are widely us ..."
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used for the numerical integration of ODEs. In this thesis, hybrid algorithms combining loworder implicit RungeKutta methods for gradient systems and quasiNewton type updates of the Jacobian matrix such as the BFGS update are considered. These hybrid algorithms numerically approximate the gradient
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