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An Algorithmic Method of Partial Derivatives [article]

Cornelius Brand, Kevin Pratt
2020 arXiv   pre-print
for testing if a linear space of matrices contains an invertible matrix (Edmonds's problem) and detecting k-internal outbranchings, and more.  ...  We also match the runtime of the fastest known deterministic algorithm for detecting subgraphs of bounded pathwidth, while using a new approach.  ...  Here Diff(f ) denotes the vector space spanned by the partial derivatives of all orders of f . is question was asked in [Pra19, estion 73], but it was not known that an answer would have algorithmic implications  ... 
arXiv:2005.05143v1 fatcat:dhvd7nftxbdw3in2gokbu2722a

A finite algorithm for the exact evaluation of higher order partial derivatives of functions of many variables

R Kalaba, L Tesfatsion, J.-L Wang
1983 Journal of Mathematical Analysis and Applications  
A formal algorithm is given for the systematic exact evaluation of higher order partial derivatives of functions of many variables. The algorithm improves upon Wengert's method in two key respects.  ...  had to be made to an automatic method of evaluating needed partial derivatives if a practical numerical tool was to be obtained.  ...  Yet, current computer method sources (e.g., [2, pp. 170-171; 5, Sect. 141) still discuss the desirability of avoiding derivative evaluations, and no presentation of such an algorithm has been found in  ... 
doi:10.1016/0022-247x(83)90266-4 fatcat:ppx2p52vxncavdj77kbmkwms6u

Search-Aware Tuning for Hierarchical Phrase-based Decoding

Feifei Zhai, Liang Huang, Kai Zhao
2015 Proceedings of the 2015 Conference on Empirical Methods in Natural Language Processing  
The recent research of "search-aware tuning" (Liu and Huang, 2014) addresses this problem by considering the partial derivations in every decoding step so that the promising ones are more likely to survive  ...  Our approach is simple to use and can be applied to most of the conventional parameter tuning methods as a plugin.  ...  Partial BLEU is quite an intuitive choice for evaluating partial derivations.  ... 
doi:10.18653/v1/d15-1149 dblp:conf/emnlp/ZhaiHZ15 fatcat:dcbijhuxmffgfmwaa3nwviq6fy

An adjoint for likelihood maximization

D. J. J. Toal, A. I. J. Forrester, N. W. Bressloff, A. J. Keane, C. Holden
2009 Proceedings of the Royal Society A  
This article derives an adjoint formulation of the likelihood employed in the construction of a kriging model via reverse algorithmic differentiation.  ...  This adjoint is found to calculate the likelihood and all of its derivatives more efficiently than the standard analytical method and can therefore be utilised within a simple local search or within a  ...  The above results indicate that the reverse algorithmic differentiation of the likelihood is the most efficient method of calculating exact partial derivatives.  ... 
doi:10.1098/rspa.2009.0096 fatcat:nypapxqbtfdpxevvnnd47kyava

From regular expressions to smaller NFAs

Pedro García, Damián López, José Ruiz, Gloria I. Álvarez
2011 Theoretical Computer Science  
Our algorithm also runs with the same time complexity of these methods. *  ...  The number of states of the automata we obtain is bounded above by the size of both the partial derivatives automaton and of the follow automaton.  ...  This method, aimed to improve the time complexity of the partial derivatives algorithm, is called the equation automaton method and when it is applied to α obtains the same automaton as the partial derivatives  ... 
doi:10.1016/j.tcs.2011.05.058 fatcat:otcqmymf4ndz5nnpx2yogfwsqe

The q-Levenberg-Marquardt method for unconstrained nonlinear optimization [article]

Danijela Protic, Miomir Stankovic
2021 arXiv   pre-print
A q-Levenberg-Marquardt method is an iterative procedure that blends a q-steepest descent and q-Gauss-Newton methods.  ...  When the current solution is far from the correct one the algorithm acts as the q-steepest descent method. Otherwise the algorithm acts as the q-Gauss-Newton method.  ...  The gradient ∇ ( ) and the Hessian ( ( )) are vectors of partial derivatives and matrix of second partial derivatives of ( ), respectively, as follows ∇ ( ) = ( ) = [ ( ) 1 ( ) 2 ⋯ ( ) ], ( ( )) = ∇ 2  ... 
arXiv:2107.03304v1 fatcat:um5wtm3qinchhpzx2gtlh3djv4

A Derivative-less Approach for Generating Phase Envelopes

Siddiqui F
2015 Oil & Gas Research  
In addition, his procedure requires the partial derivatives of fugacity, which are often difficult to get.  ...  Because the new model does not have to deal with the partial derivatives of fugacity, it can work with any EOS based phase behavior model.  ...  Additionally the bisection method does not require the partial derivatives of fugacity.  ... 
doi:10.4172/2472-0518.1000106 fatcat:binbumsdxnderi3kpsvdbvlbte

Page 4700 of Mathematical Reviews Vol. , Issue 84k [page]

1984 Mathematical Reviews  
First, an illustrative example is given focusing on the evaluation of the first few partial derivatives of a certain two-variable function. Then the general table algorithm is described.  ...  Instead of following Wengert’s method of evaluating total derivatives and recovering the partial derivatives, the table algorithm proceeds in a sequential row-by-row manner to calculate the elements of  ... 

Sum-accelerated pseudospectral methods: the Euler-accelerated sinc algorithm

John P. Boyd
1991 Applied Numerical Mathematics  
We show that the Euler summation can be applied to a standard pseudospectral scheme to produce an algorithm which is both exponentially accurate (like any other spectral method) and yet generates sparse  ...  ., Sum-accelerated pseudospectral methods: the Euler-accelerated sine algorithm, Applied Numerical Mathematics 7 (1991) 287-296 Pseudospectral discretizations of differential equations are much more accurate  ...  An obvious question is: Can one somehow combine the good features of both spectral and finite difference methods by inventing an algorithm that is both sparse and exponentially accurate?  ... 
doi:10.1016/0168-9274(91)90065-8 fatcat:pm53kkjeebfqdnrpb2nvhappta

Page 387 of International Chemical Engineering Vol. 11, Issue 3 [page]

1971 International Chemical Engineering  
Tue problem of developing an exact (reference method) means of calculating the partial derivatives of the loss of active (7) and reactive (q) power from the parameters P and Q describing an energy system  ...  Adonts SOVIET UNION An investigation of two algorithms for calculating the partial derivatives of the loss of active and reactive power from the process parameters of power systems A solution of the problem  ... 

Particle Swarm Collaborative Practicability Algorithm Based on Partial Differential Exact Solution

2017 Revista Técnica de la Facultad de Ingeniería Universidad del Zulia  
It applies the information to design the evolutionary strategy, so that the algorithm can consider both the convergence and diversity of approximate partial derivative front end.  ...  Also, the concepts of lattice dominance and lattice distance density are introduced to evaluate the personal environmental adaptability of partial derivative exact solution.  ...  IGD is an approximation of the true partial derivative to the algorithm. The lower the index value is, the better the convergence and diversity of the approximated partial derivative front end is.  ... 
doi:10.21311/001.39.11.16 fatcat:o6bgq4u4c5gkhhgo44ot4crofy

Fast Sub-aperture Stitching Algorithm Using Partial Derivatives

Yiwei Chen, Erlong Miao, Yongxin Sui, Huaijiang Yang
2015 Journal of the Optical Society of Korea  
We use partial derivatives of measurement data to separately solve piston, tilt, and defocus errors.  ...  Although simulation results indicate that the accuracy of the new algorithm is lower than the current algorithm in all 20 simulations, our experimental results validate the algorithm and show it is sufficiently  ...  Actually, using the least-squares method after calculating the partial derivative of data is just averaging, so it makes the algorithm faster than current algorithm.  ... 
doi:10.3807/josk.2015.19.1.084 fatcat:salrn6iyynbt5ercla5n4vzmoq

Computation of partial derivatives of Rayleigh-wave phase velocity using second-order subdeterminants

M. Cercato
2007 Geophysical Journal International  
Analytical methods exist to calculate the partial derivatives of phase-velocity dispersion curves.  ...  Accurate and high-speed computation of partial derivatives is recommended to achieve practical inversion algorithms.  ...  In the following, compared algorithms will be indicated with an acronym, composed of three letters representing sequentially: the initial of the first author's surname, the method adopted for partial derivative  ... 
doi:10.1111/j.1365-246x.2007.03383.x fatcat:3kzptkqkbzdfdifu65c6ymo774

Digital terrain modeling with the Chebyshev polynomials [article]

I. V. Florinsky, A. N. Pankratov
2015 arXiv   pre-print
of partial derivatives.  ...  partial derivatives of elevation.  ...  of partial derivatives.  ... 
arXiv:1507.03960v2 fatcat:hewg56yav5cstku4mv626zzi3q

Page 3941 of Mathematical Reviews Vol. , Issue 91G [page]

1991 Mathematical Reviews  
Summary: “The alternating-direction collocation (ADC) method is an efficient numerical approximation technique for the solution of parabolic partial differential equations.  ...  Summary: “The alternating-direction collocation (ADC) method combines the attractive computational features of a collocation spatial approximation and an alternating-direction time march- ing algorithm  ... 
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