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On the Complexity of Computing Error Bounds
 Found. Comput. Math
, 2000
"... We consider the cost of estimating an error bound for the computed solution of a system of linear equations, i.e. estimating the norm of a matrix inverse. Under some technical assumptions we show that computing even a coarse error bound for the solution of a triangular system of equations costs at l ..."
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We consider the cost of estimating an error bound for the computed solution of a system of linear equations, i.e. estimating the norm of a matrix inverse. Under some technical assumptions we show that computing even a coarse error bound for the solution of a triangular system of equations costs
Computing Error Bounds For Images On High Dynamic
"... INTRODUCTION The goal of this project is to compute a bound on the minimum error inherent in rendering a floating point image on a high dynamic range (HDR) display. The standard methods for rendering to this and similar devices will need to be real time. While they will employ the computation power ..."
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INTRODUCTION The goal of this project is to compute a bound on the minimum error inherent in rendering a floating point image on a high dynamic range (HDR) display. The standard methods for rendering to this and similar devices will need to be real time. While they will employ the computation
A Computable Error Bound For Matrix Functionals
 J. Comput. Appl. Math
, 1999
"... . Many problems in applied mathematics require the evaluation of matrix functionals of the form F (A) := u T f(A)u, where A is a large symmetric matrix and u is a vector. Golub and collaborators have described how approximations of such functionals can be computed inexpensively by using the Lanczo ..."
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the Lanczos algorithm. The present note shows that error bounds for these approximations can be computed essentially for free when bounds for derivatives of f on an interval containing the spectrum of A are available. 1. Introduction. The evaluation of matrix functionals of the form F (A) := u T f(A)u; A
COMPUTABLE ERROR BOUNDS WITH IMPROVED APPLICABILITY CONDITIONS FOR COLLOCATION METHODS
, 1998
"... ABSTRACT. This paper is concerned with error bounds for numerical solution of linear ordinary differential equation using collocation method. It is shown that if the differential operator is split in different operator forms then the applicability conditions for the computable error bounds which ar ..."
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ABSTRACT. This paper is concerned with error bounds for numerical solution of linear ordinary differential equation using collocation method. It is shown that if the differential operator is split in different operator forms then the applicability conditions for the computable error bounds which
INVERSION ALGORITHM WITH COMPUTABLE ERROR BOUNDS AND ITS FINANCIAL APPLICATIONS
"... In this paper we propose an inversion algorithm with computable error bounds for twodimensional, twosided Laplace transforms. The algorithm consists of two discretization parameters and two truncation parameters. Based on the computable error bounds, we can select these parameters appropriately ..."
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In this paper we propose an inversion algorithm with computable error bounds for twodimensional, twosided Laplace transforms. The algorithm consists of two discretization parameters and two truncation parameters. Based on the computable error bounds, we can select these parameters appropriately
COMPUTABLE ERROR BOUNDS FOR FINITE ELEMENT APPROXIMATION ON NONPOLYGONAL DOMAINS
"... Abstract. Fully computable, guaranteed bounds are obtained on the error in the finite element approximation which take the effect of the boundary approximation into account. We consider the case of piecewise affine approximation of the Poisson problem with pure Neumann boundary data, and obtain a fu ..."
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Abstract. Fully computable, guaranteed bounds are obtained on the error in the finite element approximation which take the effect of the boundary approximation into account. We consider the case of piecewise affine approximation of the Poisson problem with pure Neumann boundary data, and obtain a
Computational error bounds for multiple or nearly multiple eigenvalues. Linear Algebra and its Applications
, 2001
"... Abstract. In this paper bounds for clusters of eigenvalues of nonselfadjoint matrices are investigated. We describe a method for the computation of rigorous error bounds for multiple or nearly multiple eigenvalues, and for a basis of the corresponding invariant subspaces. The input matrix may be re ..."
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Cited by 9 (4 self)
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Abstract. In this paper bounds for clusters of eigenvalues of nonselfadjoint matrices are investigated. We describe a method for the computation of rigorous error bounds for multiple or nearly multiple eigenvalues, and for a basis of the corresponding invariant subspaces. The input matrix may
Reasoning the fast and frugal way: Models of bounded rationality
 Psychological Review
, 1996
"... Humans and animals make inferences about the world under limited time and knowledge. In contrast, many models of rational inference treat the mind as a Laplacean Demon, equipped with unlimited time, knowledge, and computational might. Following H. Simon’s notion of satisficing, the authors have prop ..."
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Cited by 585 (29 self)
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Humans and animals make inferences about the world under limited time and knowledge. In contrast, many models of rational inference treat the mind as a Laplacean Demon, equipped with unlimited time, knowledge, and computational might. Following H. Simon’s notion of satisficing, the authors have
Surface Simplification Using Quadric Error Metrics
"... Many applications in computer graphics require complex, highly detailed models. However, the level of detail actually necessary may vary considerably. To control processing time, it is often desirable to use approximations in place of excessively detailed models. We have developed a surface simplifi ..."
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Cited by 1169 (16 self)
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Many applications in computer graphics require complex, highly detailed models. However, the level of detail actually necessary may vary considerably. To control processing time, it is often desirable to use approximations in place of excessively detailed models. We have developed a surface
Results 1  10
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