Roundoff Error in Computing Derivatives Using the Chebyshev Differentiation Matrix

Alvin Bayliss; Andreas Class; Bernard J. Matkowsky

doi:10.1006/jcph.1995.1036

Roundoff Error in Computing Derivatives Using the Chebyshev Differentiation Matrix

Journal of Computational Physics ◽

10.1006/jcph.1995.1036 ◽

1995 ◽

Vol 116 (2) ◽

pp. 380-383 ◽

Cited By ~ 49

Author(s):

Alvin Bayliss ◽

Andreas Class ◽

Bernard J. Matkowsky

Keyword(s):

Roundoff Error ◽

Differentiation Matrix ◽

Chebyshev Differentiation Matrix

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Mapped barycentric Chebyshev differentiation matrix method for the solution of regular Sturm–Liouville problems

Applied Mathematics and Computation ◽

10.1016/j.amc.2010.07.027 ◽

2010 ◽

Vol 217 (5) ◽

pp. 2266-2276 ◽

Cited By ~ 6

Author(s):

Xuecang Zhang

Keyword(s):

Matrix Method ◽

Differentiation Matrix ◽

Sturm Liouville ◽

Chebyshev Differentiation Matrix

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A Unified Mode Solver for Optical Waveguides Based on Mapped Barycentric Rational Chebyshev Differentiation Matrix

Journal of Lightwave Technology ◽

10.1109/jlt.2010.2048891 ◽

2010 ◽

Vol 28 (12) ◽

pp. 1802-1810 ◽

Cited By ~ 2

Author(s):

Jianxin Zhu ◽

Xuecang Zhang ◽

Rencheng Song

Keyword(s):

Optical Waveguides ◽

Differentiation Matrix ◽

Mode Solver ◽

Chebyshev Differentiation Matrix ◽

Rational Chebyshev

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Stable fractional Chebyshev differentiation matrix for the numerical solution of multi-order fractional differential equations

Nonlinear Dynamics ◽

10.1007/s11071-017-3654-3 ◽

2017 ◽

Vol 90 (1) ◽

pp. 185-201 ◽

Cited By ~ 30

Author(s):

Arman Dabiri ◽

Eric A. Butcher

Keyword(s):

Differential Equations ◽

Numerical Solution ◽

Fractional Differential Equations ◽

Differentiation Matrix ◽

Fractional Differential ◽

Chebyshev Differentiation Matrix

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Roundoff error analysis of fast DCT algorithms in fixed point arithmetic

Numerical Algorithms ◽

10.1007/s11075-007-9123-1 ◽

2007 ◽

Vol 46 (1) ◽

pp. 1-22 ◽

Cited By ~ 1

Author(s):

Katja Ihsberner

Keyword(s):

Fixed Point ◽

Error Analysis ◽

Roundoff Error ◽

Roundoff Error Analysis ◽

Fixed Point Arithmetic ◽

Point Arithmetic

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Roundoff-error reduction for evaluation of a function by polynomial approximation with error feedback in fixed-point arithmetic

IEEE Transactions on Signal Processing ◽

10.1109/78.215314 ◽

1993 ◽

Vol 41 (5) ◽

pp. 1953-1955 ◽

Cited By ~ 1

Author(s):

N. Mikami ◽

M. Kobayashi ◽

Y. Yokoyama

Keyword(s):

Fixed Point ◽

Polynomial Approximation ◽

Error Reduction ◽

Roundoff Error ◽

Error Feedback ◽

Fixed Point Arithmetic ◽

Point Arithmetic

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Periodic steady-state solutions of nonlinear circuits based on a differentiation matrix

Proceedings of 2010 IEEE International Symposium on Circuits and Systems ◽

10.1109/iscas.2010.5536958 ◽

2010 ◽

Cited By ~ 2

Author(s):

Norberto Garcia

Keyword(s):

Steady State ◽

Nonlinear Circuits ◽

Differentiation Matrix ◽

Periodic Steady State ◽

Steady State Solutions

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Certified Roundoff Error Bounds Using Bernstein Expansions and Sparse Krivine-Stengle Representations

2017 IEEE 24th Symposium on Computer Arithmetic (ARITH) ◽

10.1109/arith.2017.36 ◽

2017 ◽

Cited By ~ 3

Author(s):

Alexandre Rocca ◽

Victor Magron ◽

Thao Dang

Keyword(s):

Error Bounds ◽

Roundoff Error

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Fractional pseudospectral integration/differentiation matrix and fractional differential equations

Applied Mathematics and Computation ◽

10.1016/j.amc.2018.08.044 ◽

2019 ◽

Vol 343 ◽

pp. 314-327 ◽

Cited By ~ 1

Author(s):

Saeid Gholami ◽

Esmail Babolian ◽

Mohammad Javidi

Keyword(s):

Differential Equations ◽

Fractional Differential Equations ◽

Differentiation Matrix ◽

Fractional Differential

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Roundoff-Error-Free Basis Updates of LU Factorizations for the Efficient Validation of Optimality Certificates

SIAM Journal on Matrix Analysis and Applications ◽

10.1137/16m1089630 ◽

2017 ◽

Vol 38 (3) ◽

pp. 829-853 ◽

Cited By ~ 4

Author(s):

Adolfo R. Escobedo ◽

Erick Moreno-Centeno

Keyword(s):

Roundoff Error ◽

Free Basis

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Roundoff Error

Encyclopedia of Operations Research and Management Science ◽

10.1007/978-1-4419-1153-7_200725 ◽

2013 ◽

pp. 1347-1347

Keyword(s):

Roundoff Error

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