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Roundoff and Truncation Errors
"... • Understanding the distinction between accuracy and precision • Learning how to quantify error • Learning how error estimates can be used to decide when to terminate an iterative calculation • Understanding how roundoff errors occur because digital computers have a limited ability to represent numb ..."
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numbers • Understanding why floating-point numbers have limits on their range and precision NM – Berlin Chen 2 dv dt vt v ti1 v ti ti1 ti Chapter Objectives (2/2) • Recognizing that truncation errors occur when exact mathematical formulations are represented by approximations • Knowing how to use
MINIMIZATION OF THE TRUNCATION ERROR BY GRID ADAPTATION
, 1999
"... A new grid adaptation strategy, which minimizes the truncation error of a pth-order finite difference approximation, is proposed. The main idea of the method is based on the observation that the global truncation error associated with discretization on nonuniform meshes can be minimized if the inter ..."
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Cited by 5 (1 self)
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A new grid adaptation strategy, which minimizes the truncation error of a pth-order finite difference approximation, is proposed. The main idea of the method is based on the observation that the global truncation error associated with discretization on nonuniform meshes can be minimized
Truncation Errors for Infinite Linear Systems
, 1983
"... An upper and a lower bound for the ^-norm of the difference between solutions of a countable infinite linear differential system and a corresponding finite truncated system are obtained. These bounds are uniformly bounded or decrease exponentially in time, unlike the evaluations of Chew, Skivakumar, ..."
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, & Williams (1980). The hypotheses allow the infinite system to be written as a differential equation in (x. An upper bound for the truncation error of infinite algebraic systems which can be written as linear equations in € " is also derived.
THE REDUCTION OF TRUNCATION ERROR BY EXTRAPOLATION TECHNIQUES ’
, 1961
"... By the use of two separate mesh sizes instead of OIICL irl+cornputirlg finite differences, an extrapolation to effective “zero ” mesh size may be made in order to reduce the truncation error, as originally suggesttd by Richardson. This technique of “difference extrapolation ” is applied to the? esti ..."
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By the use of two separate mesh sizes instead of OIICL irl+cornputirlg finite differences, an extrapolation to effective “zero ” mesh size may be made in order to reduce the truncation error, as originally suggesttd by Richardson. This technique of “difference extrapolation ” is applied to the
On the accuracy of multigrid truncation error estimates, Elec
- Trans. Num. Anal
"... Abstract. In solving boundary-value problems, multigrid methods can provide computable estimates of the truncation error by comparing discretizations on grids of different mesh sizes. In the standard formulation, such estimates are contaminated by errors larger than the truncation error itself unles ..."
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Cited by 2 (0 self)
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Abstract. In solving boundary-value problems, multigrid methods can provide computable estimates of the truncation error by comparing discretizations on grids of different mesh sizes. In the standard formulation, such estimates are contaminated by errors larger than the truncation error itself
Truncation- Error-Tolerant Adder 1
, 2012
"... In this study, we have proposed an architecture for high speed Truncation Adder Algorithm. In modern VLSI technology, the occurrence of all kinds of errors has become inevitable. By adopting an emerging concept in VLSI design and test, error tolerance (ET), a novel errortolerant adder (ETA) is propo ..."
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In this study, we have proposed an architecture for high speed Truncation Adder Algorithm. In modern VLSI technology, the occurrence of all kinds of errors has become inevitable. By adopting an emerging concept in VLSI design and test, error tolerance (ET), a novel errortolerant adder (ETA
Truncation errors in finite difference models for
, 1997
"... solute transport equation with first-order reaction ..."
Improved convergence rates for the truncation error in geoid determination
- Journal of Geodesy
, 2000
"... Abstract. When Stokes’s integral is used over a spherical cap to compute a gravimetric estimate of the geoid, a truncation error results due to the neglect of gravity data over the remainder of the Earth. Associated with the truncation error is an error kernel defined over these two complementary re ..."
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Cited by 7 (4 self)
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Abstract. When Stokes’s integral is used over a spherical cap to compute a gravimetric estimate of the geoid, a truncation error results due to the neglect of gravity data over the remainder of the Earth. Associated with the truncation error is an error kernel defined over these two complementary
C.Karanikas, Truncation Error on Wavelet sampling Expansions
- J. Computational Anal. and Applications
"... We estimate the truncation error of sampling expansions on translation invariant spaces, generated by integer translations of a single function and on wavelet subspaces of L2(R). As a byproduct of the main result, we get the classical D.Jagerman’s bound for Shannon’s sampling expansions. We also exa ..."
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Cited by 2 (1 self)
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We estimate the truncation error of sampling expansions on translation invariant spaces, generated by integer translations of a single function and on wavelet subspaces of L2(R). As a byproduct of the main result, we get the classical D.Jagerman’s bound for Shannon’s sampling expansions. We also
Truncation Error and Oscillation Property of the Combined Compact Difference Scheme
, 2001
"... We derive truncation error representation for the sixth order combined compact difference (CCD) scheme for discretizing a one dimensional partial differential equation. ..."
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Cited by 3 (1 self)
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We derive truncation error representation for the sixth order combined compact difference (CCD) scheme for discretizing a one dimensional partial differential equation.
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