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An Algorithmic Method of Partial Derivatives
[article]

2020
*
arXiv
*
pre-print

for testing if a linear space

arXiv:2005.05143v1
fatcat:dhvd7nftxbdw3in2gokbu2722a
*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 ...##
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A finite algorithm for the exact evaluation of higher order partial derivatives of functions of many variables

1983
*
Journal of Mathematical Analysis and Applications
*

A formal

doi:10.1016/0022-247x(83)90266-4
fatcat:ppx2p52vxncavdj77kbmkwms6u
*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 ...##
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Search-Aware Tuning for Hierarchical Phrase-based Decoding

2015
*
Proceedings of the 2015 Conference on Empirical Methods in Natural Language Processing
*

The recent research

doi:10.18653/v1/d15-1149
dblp:conf/emnlp/ZhaiHZ15
fatcat:dcbijhuxmffgfmwaa3nwviq6fy
*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*. ...##
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An adjoint for likelihood maximization

2009
*
Proceedings of the Royal Society A
*

This article

doi:10.1098/rspa.2009.0096
fatcat:nypapxqbtfdpxevvnnd47kyava
*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*. ...##
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From regular expressions to smaller NFAs

2011
*
Theoretical Computer Science
*

Our

doi:10.1016/j.tcs.2011.05.058
fatcat:otcqmymf4ndz5nnpx2yogfwsqe
*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*...##
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The q-Levenberg-Marquardt method for unconstrained nonlinear optimization
[article]

2021
*
arXiv
*
pre-print

A q-Levenberg-Marquardt

arXiv:2107.03304v1
fatcat:um5wtm3qinchhpzx2gtlh3djv4
*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 ...##
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A Derivative-less Approach for Generating Phase Envelopes

2015
*
Oil & Gas Research
*

In addition, his procedure requires the

doi:10.4172/2472-0518.1000106
fatcat:binbumsdxnderi3kpsvdbvlbte
*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. ...##
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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*...##
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Sum-accelerated pseudospectral methods: the Euler-accelerated sinc algorithm

1991
*
Applied Numerical Mathematics
*

We show that the Euler summation can be applied to a standard pseudospectral scheme to produce

doi:10.1016/0168-9274(91)90065-8
fatcat:pm53kkjeebfqdnrpb2nvhappta
*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? ...##
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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 ...##
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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

doi:10.21311/001.39.11.16
fatcat:o6bgq4u4c5gkhhgo44ot4crofy
*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. ...##
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Fast Sub-aperture Stitching Algorithm Using Partial Derivatives

2015
*
Journal of the Optical Society of Korea
*

We use

doi:10.3807/josk.2015.19.1.084
fatcat:salrn6iyynbt5ercla5n4vzmoq
*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*. ...##
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Computation of partial derivatives of Rayleigh-wave phase velocity using second-order subdeterminants

2007
*
Geophysical Journal International
*

Analytical

doi:10.1111/j.1365-246x.2007.03383.x
fatcat:3kzptkqkbzdfdifu65c6ymo774
*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*...##
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Digital terrain modeling with the Chebyshev polynomials
[article]

2015
*
arXiv
*
pre-print

*of*

*partial*

*derivatives*. ...

*partial*

*derivatives*

*of*elevation. ...

*of*

*partial*

*derivatives*. ...

##
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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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