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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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Cited by 10 (2 self)
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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
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
A Limited Memory Algorithm for Bound Constrained Optimization
 SIAM Journal on Scientific Computing
, 1994
"... An algorithm for solving large nonlinear optimization problems with simple bounds is described. ..."
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Cited by 557 (9 self)
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An algorithm for solving large nonlinear optimization problems with simple bounds is described.
Space/Time Tradeoffs in Hash Coding with Allowable Errors
 Communications of the ACM
, 1970
"... this paper tradeoffs among certain computational factors in hash coding are analyzed. The paradigm problem considered is that of testing a series of messages onebyone for membership in a given set of messages. Two new hash coding methods are examined and compared with a particular conventional h ..."
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Cited by 2067 (0 self)
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hashcoding method. The computational factors considered are the size of the hash area (space), the time required to identify a message as a nonmember of the given set (reject time), and an allowable error frequency
Good ErrorCorrecting Codes based on Very Sparse Matrices
, 1999
"... We study two families of errorcorrecting codes defined in terms of very sparse matrices. "MN" (MacKayNeal) codes are recently invented, and "Gallager codes" were first investigated in 1962, but appear to have been largely forgotten, in spite of their excellent properties. The ..."
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Cited by 741 (23 self)
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We study two families of errorcorrecting codes defined in terms of very sparse matrices. "MN" (MacKayNeal) codes are recently invented, and "Gallager codes" were first investigated in 1962, but appear to have been largely forgotten, in spite of their excellent properties
Results 1  10
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2,788,787