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Inexact QuasiNewton methods for sparse systems of nonlinear equations
"... In this paper we present the results obtained in solving consistent sparse systems of n nonlinear equations F (x) = 0; by a QuasiNewton method combined with a p block iterative rowprojection linear solver of Cimminotype, 1 p n: Under weak regularity conditions for F; it is proved that this Ine ..."
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In this paper we present the results obtained in solving consistent sparse systems of n nonlinear equations F (x) = 0; by a QuasiNewton method combined with a p block iterative rowprojection linear solver of Cimminotype, 1 p n: Under weak regularity conditions for F; it is proved
Inexact QuasiNewton methods for sparse systems of nonlinear equations
"... In this paper we present the results obtained in solving consistent sparse systems of n nonlinear equations F (x) = 0; by a QuasiNewton method combined with a p block iterative rowprojection linear solver of Cimminotype, 1 p n: Under weak regularity conditions for F; it is proved that this Inexa ..."
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In this paper we present the results obtained in solving consistent sparse systems of n nonlinear equations F (x) = 0; by a QuasiNewton method combined with a p block iterative rowprojection linear solver of Cimminotype, 1 p n: Under weak regularity conditions for F; it is proved
Inexact Block QuasiNewton Methods For Sparse Systems Of Nonlinear Equations.
, 2000
"... . In this paper we present the results obtained in solving consistent sparse systems of n nonlinear equations F (x) = 0; by a QuasiNewton method combined with a p block iterative rowprojection linear solver of Cimminotype, 1 p ø n: Under weak regularity conditions for F; it is proved that this I ..."
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Cited by 2 (2 self)
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. In this paper we present the results obtained in solving consistent sparse systems of n nonlinear equations F (x) = 0; by a QuasiNewton method combined with a p block iterative rowprojection linear solver of Cimminotype, 1 p ø n: Under weak regularity conditions for F; it is proved
QuasiNewton preconditioners for the inexact Newton method, Electronic Trans
 Num. Anal
"... Abstract. In this paper preconditioners for solving the linear systems of the Newton method in each nonlinear iteration are studied. In particular, we dene a sequence of preconditioners built by means of Broydentype rankone updates. Optimality conditions are derived which guarantee that the precon ..."
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Cited by 12 (5 self)
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that the preconditioned matrices are not far from the identity in a matrix norm. Some notes on the implementation of the corresponding inexact Newton method are given and some numerical results on two model problems illustrate the application of the proposed preconditioners. Key words. QuasiNewton method, Krylov
Practical quasiNewton methods for solving nonlinear systems
, 2000
"... Practical quasiNewton methods for solving nonlinear systems are surveyed. The definition of quasiNewton methods that includes Newton 's method as a particular case is adopted. However, especial emphasis is given to the methods that satisfy the secant equation at every iteration, which are ..."
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Cited by 14 (2 self)
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Practical quasiNewton methods for solving nonlinear systems are surveyed. The definition of quasiNewton methods that includes Newton 's method as a particular case is adopted. However, especial emphasis is given to the methods that satisfy the secant equation at every iteration, which
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
Globally convergent inexact quasiNewton methods for solving nonlinear systems
, 2002
"... Large scale nonlinear systems of equations can be solved by means of inexact quasiNewton methods. A global convergence theory is introduced that guarantees that, under reasonable assumptions, the algorithmic sequence converges to a solution of the problem. Under additional standard assumptions, ..."
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Cited by 5 (0 self)
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Large scale nonlinear systems of equations can be solved by means of inexact quasiNewton methods. A global convergence theory is introduced that guarantees that, under reasonable assumptions, the algorithmic sequence converges to a solution of the problem. Under additional standard assumptions
Truncated Block Newton and quasiNewton methods for sparse systems of nonlinear equations. Experiments on parallel platforms
, 1997
"... this paper we solve them concurrently with the iterative Lanczos algorithm LSQR [6]. Some limitations in terms of speedup efficiency were detected while using this solver (see in the section 5), in that it is an essentially sequential procedure, except the BLAS2 kernels (sparse matvet). Other choic ..."
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Cited by 4 (3 self)
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choices are possible, like the augmented system approach used in [1], or the normal equations used in [2], or the sparse QR solver [5]. Experiments with this last solver are presently under work. 3 Inexact Newton method
Sparse Bayesian Learning and the Relevance Vector Machine
, 2001
"... This paper introduces a general Bayesian framework for obtaining sparse solutions to regression and classication tasks utilising models linear in the parameters. Although this framework is fully general, we illustrate our approach with a particular specialisation that we denote the `relevance vec ..."
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Cited by 958 (5 self)
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This paper introduces a general Bayesian framework for obtaining sparse solutions to regression and classication tasks utilising models linear in the parameters. Although this framework is fully general, we illustrate our approach with a particular specialisation that we denote the `relevance
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