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Efficient Newton Steps without Jacobians
"... The computation of Newton steps (NS) is a common subproblem in iterative numerical algorithms. The usual approach requires the calculation of the Jacobian and then the solution of a linear system. The automatic differentiation (AD) technique provides an efficient way to compute a Jacobian, in partic ..."
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The computation of Newton steps (NS) is a common subproblem in iterative numerical algorithms. The usual approach requires the calculation of the Jacobian and then the solution of a linear system. The automatic differentiation (AD) technique provides an efficient way to compute a Jacobian
Approximation of the Newton Step by a Defect Correction Process
, 1999
"... In this paper, an optimal control problem governed by a partial differential equation is considered. The Newton step for this system can be computed by solving a coupled system of equations. To do this efficiently with an iterative defect correction process, a modifying operator is introduced into t ..."
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Cited by 1 (0 self)
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In this paper, an optimal control problem governed by a partial differential equation is considered. The Newton step for this system can be computed by solving a coupled system of equations. To do this efficiently with an iterative defect correction process, a modifying operator is introduced
Approximation of the Newton Step by a Defect Correction Process
, 1999
"... In this paper, an optimal control problem governed by a partial differential equation is considered. The Newton step for this system can be computed by solving a coupled system of equations. To do this efficiently with an iterative defect correction process, a modifying operator is introduced into t ..."
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In this paper, an optimal control problem governed by a partial differential equation is considered. The Newton step for this system can be computed by solving a coupled system of equations. To do this efficiently with an iterative defect correction process, a modifying operator is introduced
February 1999APPROXIMATION OF THE NEWTON STEP BY A DEFECT CORRECTION PROCESS
"... Abstract. In this paper, an optimal control problem governed by a partial differential equation is considered. The Newton step for this system can be computed by solving a coupled system of equations. To do this efficiently with an iterative defect correction process, a modifying operator is introdu ..."
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Abstract. In this paper, an optimal control problem governed by a partial differential equation is considered. The Newton step for this system can be computed by solving a coupled system of equations. To do this efficiently with an iterative defect correction process, a modifying operator
A SUFFICIENTLY EXACT INEXACT NEWTON STEP BASED ON REUSING MATRIX INFORMATION
, 2009
"... Newton’s method is a classical method for solving a nonlinear equation F (z) = 0. We derive inexact Newton steps that lead to an inexact Newton method, applicable near a solution. The method is based on solving for a particular F ′(zk′) during p consecutive iterations k = k ′ , k ′ + 1,..., k ′ + p ..."
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Newton’s method is a classical method for solving a nonlinear equation F (z) = 0. We derive inexact Newton steps that lead to an inexact Newton method, applicable near a solution. The method is based on solving for a particular F ′(zk′) during p consecutive iterations k = k ′ , k ′ + 1,..., k
An Infeasible InteriorPoint Algorithm with fullNewton Step for Linear Optimization
"... In this paper we present an infeasible interiorpoint algorithm for solving linear optimization problems. This algorithm is obtained by modifying the search direction in the algorithm [8]. The analysis of our algorithm is much simpler than that of the algorithm [8] at some places. The iteration boun ..."
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In this paper we present an infeasible interiorpoint algorithm for solving linear optimization problems. This algorithm is obtained by modifying the search direction in the algorithm [8]. The analysis of our algorithm is much simpler than that of the algorithm [8] at some places. The iteration bound of the algorithm is as good as the best known iteration bound O ( n log 1 ε for IIPMs.
A fullNewton step O(n) infeasible interiorpoint algorithm for linear optimization
, 2005
"... We present a primaldual infeasible interiorpoint algorithm. As usual, the algorithm decreases the duality gap and the feasibility residuals at the same rate. Assuming that an optimal solution exists it is shown that at most O(n) iterations suffice to reduce the duality gap and the residuals by the ..."
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Cited by 15 (7 self)
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dual problem. A special feature of the algorithm is that it uses only fullNewton steps. Two types of fullNewton steps are used, socalled feasibility steps and usual (centering) steps. Starting at strictly feasible iterates of a perturbed pair, (very) close its central path, feasibility steps serve
Bundle Adjustment  A Modern Synthesis
 VISION ALGORITHMS: THEORY AND PRACTICE, LNCS
, 2000
"... This paper is a survey of the theory and methods of photogrammetric bundle adjustment, aimed at potential implementors in the computer vision community. Bundle adjustment is the problem of refining a visual reconstruction to produce jointly optimal structure and viewing parameter estimates. Topics c ..."
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Cited by 555 (12 self)
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covered include: the choice of cost function and robustness; numerical optimization including sparse Newton methods, linearly convergent approximations, updating and recursive methods; gauge (datum) invariance; and quality control. The theory is developed for general robust cost functions rather than
COMPUTATION OF THE NEWTON STEP FOR THE EVEN AND ODD CHARACTERISTIC POLYNOMIALS OF A SYMMETRIC POSITIVE DEFINITE TOEPLITZ MATRIX
"... Abstract. We compute the Newton step for the characteristic polynomial andfortheevenandoddcharacteristic polynomials of a symmetric positive definite Toeplitz matrix as the reciprocal of the trace of an appropriate matrix. We show that, after the Yule–Walker equations are solved, this trace can be c ..."
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Cited by 1 (0 self)
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Abstract. We compute the Newton step for the characteristic polynomial andfortheevenandoddcharacteristic polynomials of a symmetric positive definite Toeplitz matrix as the reciprocal of the trace of an appropriate matrix. We show that, after the Yule–Walker equations are solved, this trace can
Results 1  10
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