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Nomenclature A = Jacobian matrix
"... We address the problem of propagating input uncertainties through a computational fluid dynamics model. Methods such as Monte Carlo simulation can require many thousands (or more) of computational fluid dynamics solves, rendering them prohibitively expensive for practical applications. This expense ..."
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We address the problem of propagating input uncertainties through a computational fluid dynamics model. Methods such as Monte Carlo simulation can require many thousands (or more) of computational fluid dynamics solves, rendering them prohibitively expensive for practical applications. This expense can be overcome with reducedorder models that preserve the essential flow dynamics. The specific contributions of this paper are as follows: first, to derive a linearized computational fluid dynamics model that permits the effects of geometry variations to be represented with an explicit affine function; second, to propose an adaptive sampling method to derive a reduced basis that is effective over the joint probability density of the geometry input parameters. The method is applied to derive efficient reduced models for probabilistic analysis of a twodimensional problem governed by the linearized Euler equations. Reducedorder models that achieve 3ordersofmagnitude reduction in the number of states are shown to accurately reproduce computational fluid dynamics Monte Carlo simulation results at a fraction of the computational cost.
Indecomposability of polynomials via Jacobian matrix
 Journal of Algebra
"... Abstract. Indecomposable polynomials are a special class of absolutely irreducible polynomials. Some improvements of important effective results on absolute irreducibility have recently appeared using Ruppert’s matrix. In a similar way, we show in this paper that the use of a Jacobian matrix gives s ..."
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Cited by 6 (3 self)
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Abstract. Indecomposable polynomials are a special class of absolutely irreducible polynomials. Some improvements of important effective results on absolute irreducibility have recently appeared using Ruppert’s matrix. In a similar way, we show in this paper that the use of a Jacobian matrix gives
1. Adjoint model and Jacobian matrix
"... A coarse grid threedimensional global inverse model of the ..."
Computing A Sparse Jacobian Matrix By Rows And Columns
, 1995
"... this paper we show that it is possible to exploit sparsity both in columns and rows by employing the forward and the reverse mode of Automatic differentiation. A graphtheoretic characterization of the problem is given. KEY WORDS: AD, Forward and Reverse mode, Nonlinear Optimization, Numerical Diffe ..."
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Cited by 25 (4 self)
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Differences, Sparsity. 1 INTRODUCTION In many nonlinear optimization problems one often needs to estimate the Jacobian matrix of a nonlinear function F : R
An Efficient Method to Compute the Inverse Jacobian Matrix in Visual Servoing
 IN ICRA
, 2004
"... The paper presents a method for estimating the inverse Jacobian matrix of a function, without computing the direct Jacobian matrix. The resulting inverse Jacobian matrix is shown to perform much better in modelling a relation # = f (x) than the classical MoorePenrose inverse J f . Theoretical ..."
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Cited by 17 (3 self)
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The paper presents a method for estimating the inverse Jacobian matrix of a function, without computing the direct Jacobian matrix. The resulting inverse Jacobian matrix is shown to perform much better in modelling a relation # = f (x) than the classical MoorePenrose inverse J f
NewtonRaphson State Estimation Solution Employing Systematically Constructed Jacobian Matrix
"... Abstract—NewtonRaphson State Estimation method using bus admittance matrix remains as an efficient and most popular method to estimate the state variables. Elements of Jacobian matrix are computed from standard expressions which lack physical significance. In this paper, elements of the state estim ..."
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Abstract—NewtonRaphson State Estimation method using bus admittance matrix remains as an efficient and most popular method to estimate the state variables. Elements of Jacobian matrix are computed from standard expressions which lack physical significance. In this paper, elements of the state
TransmissionConstrained Inverse Residual Demand Jacobian Matrix in Electricity Markets
 IEEE TRANSACTIONS ON POWER SYSTEMS
, 2011
"... A generation firm in an electricity market may own multiple generators located at multiple locations. This paper generalizes the concept of transmissionconstrained residual demand from a single generator’s perspective to that of a generation firm. We calculate the derivative of a generation firm’s ..."
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Cited by 1 (0 self)
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inverse residual demand function, i.e., the Jacobian matrix, based on a multiparameter sensitivity analysis of the optimal power flow solution, and characterize some of its properties. This Jacobian matrix provides valuable information, such as in characterizing a generation firm’s profit maximizing
ThroughtheLens Camera Control with a Simple Jacobian Matrix
 In Proc. of Graphics Interface ’95
, 1994
"... This paper improves both the computational efficiency and numerical stability of the throughthelens camera control [5]. A simple 2m \Theta 7 Jacobian matrix is derived. The matrix equation is then solved using an efficient weighted least squares method while employing the singular value decompositi ..."
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Cited by 5 (1 self)
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This paper improves both the computational efficiency and numerical stability of the throughthelens camera control [5]. A simple 2m \Theta 7 Jacobian matrix is derived. The matrix equation is then solved using an efficient weighted least squares method while employing the singular value
Relationship formula between nonlinear polynomial equations and the corresponding Jacobian matrix
"... Permanent email: Abstract: This paper provides a general proof of a relationship theorem between nonlinear analogue polynomial equations and the corresponding Jacobian matrix, presented recently by the present author. This theorem is also verified generally effective for all nonlinear polynomial alg ..."
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Permanent email: Abstract: This paper provides a general proof of a relationship theorem between nonlinear analogue polynomial equations and the corresponding Jacobian matrix, presented recently by the present author. This theorem is also verified generally effective for all nonlinear polynomial
Optimal Faulttolerant Jacobian Matrix Generators for Redundant Manipulators
, 2011
"... The design of locally optimal faulttolerant manipulators has been previously addressed via adding constraints on the bases of a desired null space to the design constraints of the manipulators. Then by algebraic or numeric solution of the design equations, the optimal Jacobian matrix is obtained. I ..."
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Cited by 3 (1 self)
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The design of locally optimal faulttolerant manipulators has been previously addressed via adding constraints on the bases of a desired null space to the design constraints of the manipulators. Then by algebraic or numeric solution of the design equations, the optimal Jacobian matrix is obtained
Results 1  10
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