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Truncated Logarithmic Approximation

M. B. Sullivan, E. E. Swartzlander
2013 2013 IEEE 21st Symposium on Computer Arithmetic  
Index Terms-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.  ... 
doi:10.1109/arith.2013.34 dblp:conf/arith/SullivanS13 fatcat:p2tlokayevccbcjqii3ih7hgyu

Truncated Moments of Nonsinglet Parton Distributions in the double logarithmic ln^2x approximation [article]

D.Kotlorz, A.Kotlorz
2004 arXiv   pre-print
All calculations are performed within double 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.  ... 
arXiv:hep-ph/0403061v1 fatcat:y76yzczzrbc5dpwyswj4q5mgom

Truncated error correction for flexible approximate multiplication

Michael B. Sullivan, Earl E. Swartzlander
2012 2012 Conference Record of the Forty Sixth Asilomar Conference on Signals, Systems and Computers (ASILOMAR)  
Index Terms-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.  ... 
doi:10.1109/acssc.2012.6489023 dblp:conf/acssc/SullivanS12 fatcat:e7wu7gygvvgkllm4bj3yembji4

A note on Padé approximants of tensor logarithm with application to Hencky-type hyperelasticity

M. Rezaee-Hajidehi, K. Tůma, S. Stupkiewicz
2020 Computational Mechanics  
Accuracy and computational efficiency of the Padé 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.  ... 
doi:10.1007/s00466-020-01915-0 fatcat:ayr7bghky5h3rjx7oqet7b25qe

Page 774 of American Society of Civil Engineers. Proceedings of the American Society of Civil Engineers Vol. 107, Issue HY6 [page]

1881 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  ... 

A novel hybrid high-dimensional model representation (HDMR) based on the combination of plain and logarithmic high-dimensional model representations [chapter]

B. Tunga, M. Demiralp
2009 Lecture Notes in Electrical Engineering  
On the other hand, if the given function is dominantly multiplicative then the 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.  ... 
doi:10.1007/978-0-387-76483-2_9 fatcat:6h65cweh5jbkva35nxdgfijzlq

The mysteries of the best approximation and Chebyshev expansion for the function with logarithmic regularities [article]

Xiaolong Zhang
2021 arXiv   pre-print
In this paper, we find that for the functions with 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].  ... 
arXiv:2108.03836v2 fatcat:wbnjgeqzazhmxejisah5jbko3a

Weighted Prime Powers Truncation of the Asymptotic Expansion for the Logarithmic Integral: Properties and Applications [article]

Shaun R. Deaton
2021 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 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  ... 
arXiv:2103.17039v2 fatcat:gk74vqtgynd65bsfexsk6jxaky

Non-binary LDPC decoding using truncated messages in the Walsh-Hadamard domain [article]

Jossy Sayir
2014 arXiv   pre-print
In this paper, we demonstrate that considerable savings can be achieved by letting WH based decoders operate on 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.  ... 
arXiv:1407.4342v2 fatcat:nz3x5biuufagdddmapz6i2ntnm

Seismic Random Noise Attenuation in the Laplace Domain using Singular Value Decomposition

Wansoo Ha, Changsoo Shin
2021 IEEE Access  
We attenuated ambient noise in Laplace-domain 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.  ... 
doi:10.1109/access.2021.3074648 fatcat:kinbecwfjvcgxlmvpuivxcxhgy

Quantitative predictions with detuned normal forms

Giuseppe Pucacco, Dino Boccaletti, Cinzia Belmonte
2008 Celestial mechanics & dynamical astronomy  
The phase-space structure of two families of galactic potentials is 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).  ... 
doi:10.1007/s10569-008-9141-x fatcat:lhfb4xmsqrb3nn6hnsyfgv2pnm

A Two-Stage Operand Trimming Approximate Logarithmic Multiplier

Ratko Pilipovic, Patricio Bulic, Uros Lotric
2021 IEEE Transactions on Circuits and Systems Part 1: Regular Papers  
We present an 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.  ... 
doi:10.1109/tcsi.2021.3069168 fatcat:ne27ilssxvbudch7kjeocgsv5i

Linear and Quadratic Interpolators Using Truncated-Matrix Multipliers and Squarers

E. Walters III
2015 Computers  
This paper presents a technique for designing linear and quadratic interpolators for function 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  ... 
doi:10.3390/computers4040293 fatcat:4yfht4pb2jawtdkbzy357uoouu

Transmutation of scale dependence into truncation uncertainty via renormalization-group improvement of theR(s)series

V. Elias, D. G. C. McKeon, T. G. Steele
2004 Physical Review D  
Consequently, the ambiguity in how the 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.  ... 
doi:10.1103/physrevd.69.045015 fatcat:ipuuwil6jnc6vcworso6fu5gnu

On the Gibbs phenomenon I: recovering exponential accuracy from the Fourier partial sum of a nonperiodic analytic function

David Gottlieb, Chi-Wang Shu, Alex Solomonoff, Hervé Vandeven
1992 Journal of Computational and Applied Mathematics  
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, 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.  ... 
doi:10.1016/0377-0427(92)90260-5 fatcat:hzwmxqbbgjb5daatwe3eiq5zym
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