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Truncated Logarithmic Approximation

2013
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2013 IEEE 21st Symposium on Computer Arithmetic
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Index Terms-

doi:10.1109/arith.2013.34
dblp:conf/arith/SullivanS13
fatcat:p2tlokayevccbcjqii3ih7hgyu
*Truncated**approximate*binary*logarithms*,*logarithm*generation, anti-*logarithm*generation, computer arithmetic, mixed precision. ... The*truncated**approximate**logarithm*simultaneously improves the efficiency and precision of Mitchell's*approximation*while remaining simple to implement. ... CONCLUSION*Truncated**approximate**logarithms*are a modification of Mitchell's algorithm for computing the*approximate*binary*logarithm*. ...##
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Truncated Moments of Nonsinglet Parton Distributions in the double logarithmic ln^2x approximation
[article]

2004
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arXiv
*
pre-print

All calculations are performed within double

arXiv:hep-ph/0403061v1
fatcat:y76yzczzrbc5dpwyswj4q5mgom
*logarithmic*ln^2x*approximation*. ... An equation for*truncated*moments which incorporates ln^2x effects is formulated and solved for the unintegrated structure function f^NS(x,Q^2). ... Some results for*truncated*momentsf NS (x 0 , n, k 2 ), F 2 NS (x 0 , n, k 2 ),ḡ 1 NS (x 0 , n, k 2 ) in the double*logarithmic*ln 2 x*approximation*. ...##
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Truncated error correction for flexible approximate multiplication

2012
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2012 Conference Record of the Forty Sixth Asilomar Conference on Signals, Systems and Computers (ASILOMAR)
*

Index Terms-

doi:10.1109/acssc.2012.6489023
dblp:conf/acssc/SullivanS12
fatcat:e7wu7gygvvgkllm4bj3yembji4
*Truncated*error correction,*approximate*binary*logarithms*,*approximate*multiplication, computer arithmetic. ... Exact*logarithmic*(and anti-*logarithmic*) conversion is prohibitively expensive for use in general multipliers; however, inexpensive estimate conversions can be used to perform*approximate*multiplication ...*Truncated*error correction extends prior work on iterative*approximate**logarithmic*multiplication, resulting in a flexible*approximate*multiplier with improved efficiency. A. ...##
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A note on Padé approximants of tensor logarithm with application to Hencky-type hyperelasticity

2020
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Computational Mechanics
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Accuracy and computational efficiency of the Padé

doi:10.1007/s00466-020-01915-0
fatcat:ayr7bghky5h3rjx7oqet7b25qe
*approximants*are favourably compared to an alternative*approximation*method employing the*truncated*Taylor series. ... We show that the*logarithmic*(Hencky) strain and its derivatives can be*approximated*, in a straightforward manner and with a high accuracy, using Padé*approximants*of the tensor (matrix)*logarithm*. ... An alternative method of*approximating*the tensor*logarithm*employs the*truncated*Taylor series. ...##
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Page 774 of American Society of Civil Engineers. Proceedings of the American Society of Civil Engineers Vol. 107, Issue HY6
[page]

1881
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American Society of Civil Engineers. Proceedings of the American Society of Civil Engineers
*

;
coefficient of association between variables;
return period, in years;
return period (not necessarily in years);
return period as

*approximation*of T),; time; natural*logarithm*of flood peaks; natural ...*logarithm*of discharge at*truncation*level; natural*logarithm*of flood volumes; flood volume in cubic meters (1 m* = 35.31 cu ft); flood volume in cubic meters per second hours (1 cubic meters per second ...##
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A novel hybrid high-dimensional model representation (HDMR) based on the combination of plain and logarithmic high-dimensional model representations
[chapter]

2009
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Lecture Notes in Electrical Engineering
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On the other hand, if the given function is dominantly multiplicative then the

doi:10.1007/978-0-387-76483-2_9
fatcat:6h65cweh5jbkva35nxdgfijzlq
*Logarithmic*HDMR method which*truncates*the scheme at a prescribed multivariance of the HDMR of the*logarithm*of the given ... High Dimensional Model Representation (HDMR) was proposed to*approximate*the multivariate functions by the functions having less number of independent variables. ... The structure developed in*Logarithmic*HDMR method allows us to define new*truncation*quality measurers which are monotonously increasing from 0 to 1 in ascending multivariance. ...##
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The mysteries of the best approximation and Chebyshev expansion for the function with logarithmic regularities
[article]

2021
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arXiv
*
pre-print

In this paper, we find that for the functions with

arXiv:2108.03836v2
fatcat:wbnjgeqzazhmxejisah5jbko3a
*logarithmic*regularities, the pointwise errors of Chebyshev*approximation*are smaller than the ones of the best*approximations*except only in the very ... The pointwise error for Chebyshev series,*truncated*at the degree n is O(n^-κ) (κ = min{2γ+1, 2δ + 1}), but is worse by one power of n in narrow boundary layer near the weak singular endpoints. ... function, the*logarithm*singular function owns a much better Chebyshev*approximation*rather than the best*approximation*for almost all values of x ∈ [−1, 1]. ...##
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Weighted Prime Powers Truncation of the Asymptotic Expansion for the Logarithmic Integral: Properties and Applications
[article]

2021
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arXiv
*
pre-print

By dropping the minimization constraint and introducing a new variable x for the number of expansion terms, consider the question: Where to

arXiv:2103.17039v2
fatcat:gk74vqtgynd65bsfexsk6jxaky
*truncate*the asymptotic expansion for the*logarithmic*integral ... There exists a closed form*approximation*that does not utilize the zeros at all. From this, a new bound is obtained on the summation ∑_ρ li(n^ρ). ... Even though for all n ≤ 25 there is not much variation, any close*approximation*to the exact*truncation*will be sufficient to obtain a suitable bound by appropriately*truncating*the*logarithmic*integral ...##
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Non-binary LDPC decoding using truncated messages in the Walsh-Hadamard domain
[article]

2014
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arXiv
*
pre-print

In this paper, we demonstrate that considerable savings can be achieved by letting WH based decoders operate on

arXiv:1407.4342v2
fatcat:nz3x5biuufagdddmapz6i2ntnm
*truncated*messages as well. ... The Extended Min-Sum (EMS) algorithm for non-binary low-density parity-check (LDPC) defined over an alphabet of size q operates on*truncated*messages of length q' to achieve a complexity of the order q ... For*truncated*messages, working in the*logarithmic*domain adds a dimension of subtelty. ...##
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Seismic Random Noise Attenuation in the Laplace Domain using Singular Value Decomposition

2021
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IEEE Access
*

We attenuated ambient noise in Laplace-domain

doi:10.1109/access.2021.3074648
fatcat:kinbecwfjvcgxlmvpuivxcxhgy
*logarithmic*wavefields by using a moving average filter and low-rank*approximation*of data matrices using the*truncated*SVD method. ... SVD can be used to*approximate*the original matrix using a low-rank matrix by*truncating*small singular values. ...##
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Quantitative predictions with detuned normal forms

2008
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Celestial mechanics & dynamical astronomy
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The phase-space structure of two families of galactic potentials is

doi:10.1007/s10569-008-9141-x
fatcat:lhfb4xmsqrb3nn6hnsyfgv2pnm
*approximated*with a resonant detuned normal form. ... Table 5 Subsequent*truncations*of continued fraction (42) with M = 14 for the*logarithmic*potential (loop). ... At order M = 4 it is Table 3 3 Subsequent*truncations*of the continued fraction (42) with M = 14 for the*logarithmic*potential (banana). ...##
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A Two-Stage Operand Trimming Approximate Logarithmic Multiplier

2021
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IEEE Transactions on Circuits and Systems Part 1: Regular Papers
*

We present an

doi:10.1109/tcsi.2021.3069168
fatcat:ne27ilssxvbudch7kjeocgsv5i
*approximate**logarithmic*multiplier with two-stage operand trimming, which prioritises area and energy consumption while retains acceptable accuracy. ... Index Terms-*Logarithmic*multiplier,*approximate*computing, arithmetic circuit design, Mitchell's multiplier, energy-efficient processing. Manuscript ... Due to mantissa*truncation*, Kim et al. achieved efficient*logarithm*and antilogarithm conversions, but at the same time, mantissa*truncation*causes a large error. ...##
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Linear and Quadratic Interpolators Using Truncated-Matrix Multipliers and Squarers

2015
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Computers
*

This paper presents a technique for designing linear and quadratic interpolators for function

doi:10.3390/computers4040293
fatcat:4yfht4pb2jawtdkbzy357uoouu
*approximation*using*truncated*multipliers and squarers. ... Initial coefficient values are found using a Chebyshev-series*approximation*and then adjusted through exhaustive simulation to minimize the maximum absolute error of the interpolator output. ... The*logarithmic*number system (LNS), which greatly reduces the area and power required for multiplication and other operations, requires*approximation*of a special*logarithm*to perform addition and subtraction ...##
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Transmutation of scale dependence into truncation uncertainty via renormalization-group improvement of theR(s)series

2004
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Physical Review D
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Consequently, the ambiguity in how the

doi:10.1103/physrevd.69.045015
fatcat:ipuuwil6jnc6vcworso6fu5gnu
*logarithm*is defined is absorbable in the uncertainty associated with*truncating*the original perturbative series after its calculationally known terms. ... However, given that the original (unimproved) series is known to third-order in α_s(μ), this*logarithm*ambiguity is shown not to enter the optimally improved summation-of-*logarithms*series until the term ...*logarithms*: S is consistent with Eq. (22), the O(x 3 )*truncation*of the unimproved series (7) evaluated at µ = √ s. ...##
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On the Gibbs phenomenon I: recovering exponential accuracy from the Fourier partial sum of a nonperiodic analytic function

1992
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Journal of Computational and Applied Mathematics
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tional and Applied Mathematics 43 (1992) 81-98. the Gibbs phenomenon I: recovering analytic function, Journal of Computa-It is well known that the Fourier series of an analytic and p(:riodic function,

doi:10.1016/0377-0427(92)90260-5
fatcat:hzwmxqbbgjb5daatwe3eiq5zym
*truncated*... In this paper we show that the first 2N + 1 Fourier coefficients contain enough information about the function, so that an exponentially convergent*approximation*(in the maximum norm) can be constructed ... Fig. 4 , again both in*logarithmic*scales. ...
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