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Journal articles on the topic "Directional derivatives":
1
Craven, B. D. "On quasidifferentiable optimization." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 41, no. 1 (August 1986): 64–78. http://dx.doi.org/10.1017/s1446788700028081.
AbstractLagrangian necessary conditions for optimality, of both Fritz John and Kuhn Tucker types, are obtained for a constrained minimization problem, where the functions are locally Lipschitz and have directional derivatives, but need not have linear Gâteaux derivatives; the variable may be constrained to lie in a nonconvex set. The directional derivatives are assumed to have some convexity properties as functions of direction; this generalizes the concept of quasidifferentiable function. The convexity is not required when directional derivatives are replaced by Clarke generalized derivatives. Sufficient Kuhn Tucker conditions, and a criterion for the locally solvable constraint qualification, are obtained for directionally differentiable functions.
2
Li, Meng, and Yi Zhan. "Integrating Feature Direction Information with a Level Set Formulation for Image Segmentation." East Asian Journal on Applied Mathematics 6, no. 1 (January 27, 2016): 1–22. http://dx.doi.org/10.4208/eajam.231114.240915a.
AbstractA feature-dependent variational level set formulation is proposed for image segmentation. Two second order directional derivatives act as the external constraint in the level set evolution, with the directional derivative across the image features direction playing a key role in contour extraction and another only slightly contributes. To overcome the local gradient limit, we integrate the information from the maximal (in magnitude) second-order directional derivative into a common variational framework. It naturally encourages the level set function to deform (up or down) in opposite directions on either side of the image edges, and thus automatically generates object contours. An additional benefit of this proposed model is that it does not require manual initial contours, and our method can capture weak objects in noisy or intensity-inhomogeneous images. Experiments on infrared and medical images demonstrate its advantages.
3
Chen, W., and Z. Ditzian. "Mixed and directional derivatives." Proceedings of the American Mathematical Society 108, no. 1 (January 1, 1990): 177. http://dx.doi.org/10.1090/s0002-9939-1990-0994773-0.
Bednařík, Dušan, and Karel Pastor. "A characterization of $C^{1,1}$ functions via lower directional derivatives." Mathematica Bohemica 134, no. 2 (2009): 217–21. http://dx.doi.org/10.21136/mb.2009.140656.
Preiss, D., and L. Zajíček. "Directional derivatives of Lipschitz functions." Israel Journal of Mathematics 125, no. 1 (December 2001): 1–27. http://dx.doi.org/10.1007/bf02773371.
Korablev, A. I. "Directional derivatives of quasiconvex functionals." Journal of Soviet Mathematics 41, no. 6 (June 1988): 1425–28. http://dx.doi.org/10.1007/bf01097072.
Ben-Tal, A., and J. Zowe. "Directional derivatives in nonsmooth optimization." Journal of Optimization Theory and Applications 47, no. 4 (December 1985): 483–90. http://dx.doi.org/10.1007/bf00942193.
Apalak, MK, and MD Demirbas. "Thermal stress analysis of in-plane two-directional functionally graded plates subjected to in-plane edge heat fluxes." Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications 232, no. 8 (April 11, 2016): 693–716. http://dx.doi.org/10.1177/1464420716643857.
This study investigates the thermal stress and deformation states of bi-directional functionally graded clamped plates subjected to constant in-plane heat fluxes along two ceramic edges. The material properties of the functionally graded plates were assumed to vary with a power law along two in-plane directions not through the plate thickness direction. The spatial derivatives of thermal and mechanical properties of the material composition were considered, and the effects of the bi-directional composition variations and spatial derivative terms on the displacement, strain and stress distributions were also investigated. The heat conduction and Navier equations describing the two-dimensional thermo-elastic problem were discretized using finite-difference method, and the set of linear equations were solved using the pseudo singular value method. The compositional gradient exponents and the spatial derivatives of thermal and mechanical properties of the material composition were observed to play an important role especially on the heat transfer durations, the displacement and strain distributions, but had a minor effect on the temperature and stress distributions.
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Ojha, Bhuwan Prasad. "Different Concepts of Derivatives." Journal of Advanced College of Engineering and Management 3 (January 10, 2018): 11. http://dx.doi.org/10.3126/jacem.v3i0.18809.
<p>In this paper, different concept of derivatives with some properties has been introduced. In differential calculus, the partial derivative, directional derivative and total derivative are studied. Their generalization for Banach spaces are the Gateaux differential and Freshet derivative.</p><p><strong>Journal of Advanced College of Engineering and Management,</strong> Vol.3, 2017, Page: 11-14</p>
Wir befassen uns mit Gleichgewichtsproblemen, die bei dem Zusammentreffen von Märkten und Marktteilnehmern entstehen, zuerst in einem Modell mit konkurrierenden Märkten mit Feedback und asymmetrischer Information und dann mit strategisch interagierenden Händlern. Zudem untersuchen wir spezielle Richtungsableitung im Kontext des pfadweisen Malliavinkalküls.
Im ersten Kapitel analysieren wir ein Prinzipal-Agenten-Problem mit einem monopolistischen Dealer, der mit einem Crossing-Netzwerk (CN) um den Handel mit Agenten mit privater Information konkurriert. Wir untersuchen die gewinnmaximierenden Angebote des Dealers für unterschiedliche Outside-Optionen und formulieren hinreichende Bedingungen für die Existenz und Eindeutigkeit einer optimalen Lösung. In unserem Modell ist die Einführung des CN für die Agenten vorteilhaft und ein Gleichgewichtspreis existiert.
Im zweiten Kapitel analysieren wir den Einfluss vergleichender Leistungsbewertung von Händlern auf die Preisfindung im Marktgleichgewicht. Ein Derivat soll einen markträumenden Preis bekommen unter Beachtung der strategisch handelnden Agenten. Das Risiko eines Händlers setzt sich aus dem eigenen Risikoprofil und dem Erfolg des Handelns relativ zum durchschnittlichen Handelserfolg aller zusammen und er wird durch eine BSDE gemessen. Wir bestimmen einen repräsentativen Agenten und zeigen so die Existenz und Eindeutigkeit eines Gleichgewichtspreises. Weiterhin können wir diesen charakterisieren und im Spezialfall von entropischen Risikomaßen konkret berechnen. In diesem Spezialfall führen wir auch eine Parameteranalyse durch.
Das dritte Kapitel verknüpft klassischen und pfadweisen Malliavinkalkül. Wir definieren und analysieren pfadweise Richtungsableitungen mit Hilfe von Perturbationen mit Cameron-Martin-Funktionen, mit (Hölder-)stetigen Funktionen, mit unstetigen Funktionen und mit Maßen. Somit sind sowohl die klassische Malliavin-Ableitung als auch Dupires vertikale Ableitung als Spezialfälle enthalten. We analyze equilibrium problems arising from interacting markets and market participants, first competing markets with feedback and asymmetric information, then strategically interacting traders; moreover we analyze a new notion of a pathwise directional derivative in the context of pathwise Malliavin calculus.
The first chapter analyzes a principal-agent game in which a monopolistic profit-maximizing dealer competes with a crossing network (CN) for trading with privately informed agents. We analyze the structure of the dealer’s offered pricing schedules for different outside options. We give sufficient conditions for the existence and uniqueness of a solution to the dealer’s problem and show that in our setting the introduction of the CN is beneficial for the agents. Additionally, we discuss existence and uniqueness of an equilibrium price for the feedback between dealer and CN.
In the second chapter we analyze the impact of performance concerns on a problem of equilibrium pricing. A derivative is priced such that the market clears, given strategically behaving agents. Their risk stems from a risky position in the future and the relative trading gains compared to all other agents. The risk measure of each agent is specified by a BSDE. In spite of the strategic interaction, we are able to apply a representative agent approach to obtain existence and uniqueness of the equilibrium market price of external risk. In the special case of entropic risk measures, we perform a parameter analysis.
The third chapter provides a link between classical and pathwise Malliavin calculus. We define and analyze pathwise directional derivatives via perturbations with Cameron-Martin functions, (Hölder-)continuous functions, discontinuous functions and measures, thereby including both the traditional Malliavin derivative and the vertical derivative from Dupire’s work.
2
Sansing, Christopher. "Directional time-frequency analysis with applications." Diss., Columbia, Mo. : University of Missouri-Columbia, 2006. http://hdl.handle.net/10355/4484.
Thesis (Ph.D.)--University of Missouri-Columbia, 2006. The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file. Title from title screen of research.pdf file viewed on (March 1, 2007) Vita. Includes bibliographical references.
3
Bielagk, Jana [Verfasser], Ulrich [Gutachter] Horst, Peter [Gutachter] Imkeller, and Traian [Gutachter] Pirvu. "Essays on Market Microstructure and Pathwise Directional Derivatives / Jana Bielagk ; Gutachter: Ulrich Horst, Peter Imkeller, Traian Pirvu." Berlin : Humboldt-Universität zu Berlin, 2018. http://d-nb.info/1185577939/34.
Serbichenko, Daria. "Modal analysis of time-dependent structures using Derictional Derivatives." Thesis, Ecole centrale de Nantes, 2019. http://www.theses.fr/2019ECDN0059.
Dans un grand nombre de domaines, l'analyse modale de structures est une composante capitale du dimensionnement. Pour l'identification des fréquences et modes propres, les logiciels de calcul éléments finis sont maintenant souvent utilisés et offrent des réponses rapides et satisfaisantes dans une grande majorité de cas. Cependant, lorsqu'une structure possède une géométrie qui varie au cours du temps ou alors lorsqu'une fissure se propage dans cette structure, les méthodes classiques employées peuvent être contraignantes et consommatrice de temps CPU (remaillage, résolution itérative de problèmes aux valeurs propres...), surtout si l'on veut suivre l'évolution des solutions propres.Dans ces travaux de doctorat, une méthode originale est proposée afin d’améliorer la gestion de l’analyse modale de structures subissant des changements de forme au cours du temps. Celle-ci est basée sur les dérivées directionnelles et sur la méthode X-FEM. En effet, les dérivées directionnelles permettent de prédire l’évolution des solutions propres entre deux configurations temporelles de la structure et X-FEM permet de s’affranchir des contraintes liées au maillage de chacune des configurations. Grâce à des critères spécifiquement développés, la méthodologie a été testée pour des cas de problèmes plans et axysymétrique. Les résultats obtenus en regard des méthodes classiques et les conclusions qu’elles peuvent amener, permettent de voir les nombreux avantages de l’outil que nous avons proposé In many industrial fields, modal analysis of structures is a primary key during the design. Finite Element Method is often used to identify both natural frequencies and shapes, offering quick and satisfactory answers in most cases. However, when a structure possesses a time-dependent geometry or if the structure is subjected to a crack propagation, the standards methods used can be constraining. They can also be CPU time consuming (due to remeshing, iterative solving of eigenvalue problems…), especially if one wants to track the evolution of the eigensolutions.In this research work, an original method is proposed to improve the management of finding the evolution of eigensolutions in case of time-dependent structures. This methology is based on the combination of directional derivatives and X-FEM. The directional derivatives allow to estimate the evolution of the eigensolutions between two configurations of the structure and X-FEM overcomes the constraints related to mesh generation of each configuration. Through specific developed criteria, the methodology has been tested for cases of plane and axisymmetric problems. The results obtained in comparison to the standard modal analyses and the conclusions that they can bring, highlight the advantages of the numerical tool that we proposed
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Bangemann, Tim Richard. "Nonlinear finite element treatment of bifurcation in the post-buckling analysis of thin elastic plates and shells." Thesis, Brunel University, 1995. http://bura.brunel.ac.uk/handle/2438/6362.
The geometrically nonlinear constant moment triangle based on the von Karman theory of thin plates is first described. This finite element, which is believed to be the simplest possible element to pass the totality of the von Karman patch test, is employed throughout the present work. It possesses the special characteristic of providing a tangent stiffness matrix which is accurate and without approximation. The stability of equilibrium of discrete conservative systems is discussed. The criteria which identify the critical points (limit and bifurcation), and the method of determination of the stability coefficients are presented in a simple matrix formulation which is suitable for computation. An alternative formulation which makes direct use of higher order directional derivatives of the total potential energy is also presented. Continuation along the stable equilibrium solution path is achieved by using a recently developed Newton method specially modified so that stable points are points of attraction. In conjunction with this solution technique, a branch switching method is introduced which directly computes any intersecting branches. Bifurcational buckling often exhibits huge structural changes and it is believed that the computation of the required switch procedure is performed here, and for the first time, in a satisfactory manner. Hence, both limit and bifurcation points can be treated without difficulty and with continuation into the post buckling regime. In this way, the ability to compute the stable equilibrium path throughout the load-deformation history is accomplished. Two numerical examples which exhibit bifurcational buckling are treated in detail and provide numerical evidence as to the ability of the employed techniques to handle even the most complex problems. Although only relatively coarse finite element meshes are used it is evident that the technique provides a powerful tool for any kind of thin elastic plate and shell problem. The thesis concludes with a proposal for an algorithm to automate the computation of the unknown parameter in the branch switching method.
6
Raihen, Nurul. "Convergence Rates for Hestenes' Gram-Schmidt Conjugate Direction Methodwithout Derivatives in Numerical Optimization." University of Toledo / OhioLINK, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=toledo1494608232437057.
ALMEIDA, Arthur Gilzeph Farias. "Existência de soluções para uma classe de problemas elípticos com não linearidade descontínua." Universidade Federal de Campina Grande, 2013. http://dspace.sti.ufcg.edu.br:8080/jspui/handle/riufcg/1389.
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Previous issue date: 2013-10 CNPq Neste trabalho estudamos a existência de, pelo menos, três soluções distintas para dois
problemas de inclusão diferencial. Para isto, faremos uso da teoria da análise convexa
para funcionais localmente Lipschitz, bem como métodos variacionais. In this work we study the existence of, at least, three distinct solutions to two problems of differential inclusion. For this, we use the theory of convex functional analysis Lipschitz locally, and variational methods.
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Zoltan, Pap. "Projektivni postupci tipa konjugovanih gradijenata za rešavanje nelinearnih monotonih sistema velikih dimenzija." Phd thesis, Univerzitet u Novom Sadu, Prirodno-matematički fakultet u Novom Sadu, 2019. https://www.cris.uns.ac.rs/record.jsf?recordId=110614&source=NDLTD&language=en.
U disertaciji su posmatrani projektivni postupci tipa konjugovanih gradijenata za rešavanje nelinearnih monotonih sistema velikih dimenzija. Ovi postupci kombinuju projektivnu metodu sa pravcima pretraživanja tipa konjugovanih gradijenata. Zbog osobine monotonosti sistema, projektivna metoda omogućava jednostavnu globalizaciju, a pravci pretraživanja tipa konjugovanih gradijenata zahtevaju maloračunarske memorije pa su pogodni za rešavanje sistema velikih dimenzija. Projektivni postupci tipa konjugovanih gradijenata ne koriste izvode niti funkciju cilja i zasnovani su samo na izračunavanju vrednosti funkcije sistema, pa su pogodni i za rešavanje neglatkih monotonih sistema. Pošto se globalna konvergencija dokazuje bez pretpostavki o regularnosti, ovi postupci se mogu koristiti i za rešavanje sistema sa singularnim rešenjima. U disertaciji su definisana tri nova tročlana pravca pretraživanjatipa Flečer-Rivs i dva nova hibridna pravca tipa Hu-Stori. Formulisani su projektivni postupci sa novim pravcima pretraživanja i dokazana je njihova globalna konvergencija. Numeričke performanse postupaka testirane su na relevantnim primerima i poređene sa poznatim postupcima iz literature. Numerički rezultati potvrđuju da su novi postupci robusni, efikasni i uporedivi sa postojećim postupcima. Projection based CG methods for solving large-scale nonlinear monotone systems are considered in this thesis. These methods combine hyperplane projection technique with conjugate gradient (CG) search directions. Hyperplane projection method is suitable for monotone systems, because it enables simply globalization, while CG directions are efficient for large-scale nonlinear systems, due to low memory. Projection based CG methods are funcion-value based, they don’t use merit function and derivatives, and because of that they are also suitable for solving nonsmooth monotone systems. The global convergence of these methods are ensured without additional regularity assumptions, so they can be used for solving singular systems.Three new three-term search directions of Fletcher-Reeves type and two new hybrid search directions of Hu-Storey type are defined. PCG algorithm with five new CG type directions is proposed and its global convergence is established. Numerical performances of methods are tested on relevant examples from literature. These results point out that new projection based CG methods have good computational performances. They are efficient, robust and competitive with other methods.
9
Portier, François. "Réduction de la dimension en régression." Phd thesis, Université Rennes 1, 2013. http://tel.archives-ouvertes.fr/tel-00871049.
Dans cette thèse, nous étudions le problème de réduction de la dimension dans le cadre du modèle de régression suivant Y=g(B X,e), où X est un vecteur de dimension p, Y appartient à R, la fonction g est inconnue et le bruit e est indépendant de X. Nous nous intéressons à l'estimation de la matrice B, de taille dxp où d est plus petit que p, (dont la connaissance permet d'obtenir de bonnes vitesses de convergence pour l'estimation de g). Ce problème est traité en utilisant deux approches distinctes. La première, appelée régression inverse nécessite la condition de linéarité sur X. La seconde, appelée semi-paramétrique ne requiert pas une telle condition mais seulement que X possède une densité lisse. Dans le cadre de la régression inverse, nous étudions deux familles de méthodes respectivement basées sur E[X f(Y)] et E[XX^T f(Y)]. Pour chacune de ces familles, nous obtenons les conditions sur f permettant une estimation exhaustive de B, aussi nous calculons la fonction f optimale par minimisation de la variance asymptotique. Dans le cadre de l'approche semi-paramétrique, nous proposons une méthode permettant l'estimation du gradient de la fonction de régression. Sous des hypothèses semi-paramétriques classiques, nous montrons la normalité asymptotique de notre estimateur et l'exhaustivité de l'estimation de B. Quel que soit l'approche considérée, une question fondamentale est soulevée : comment choisir la dimension de B ? Pour cela, nous proposons une méthode d'estimation du rang d'une matrice par test d'hypothèse bootstrap.
10
Chowdhury, Monsur. "Optimal designs for maximum likelihood estimation and factorial structure design." 2016. http://hdl.handle.net/1993/31637.
This thesis develops methodologies for the construction of various types of optimal designs with applications in maximum likelihood estimation and factorial structure design. The methodologies are applied to some real data sets throughout the thesis.
We start with a broad review of optimal design theory including various types of optimal designs along with some fundamental concepts. We then consider a class of optimization problems and determine the optimality conditions. An important tool is the directional derivative of a criterion function. We study extensively the properties of the directional derivatives. In order to determine the optimal designs, we consider a class of multiplicative algorithms indexed by a function, which satisfies certain conditions. The most important and popular design criterion in applications is D-optimality. We construct such designs for various regression models and develop some useful strategies for better convergence of the algorithms.
The remaining thesis is devoted to some important applications of optimal design theory. We first consider the problem of determining maximum likelihood estimates of the cell probabilities under the hypothesis of marginal homogeneity in a square contingency table. We formulate the Lagrangian function and remove the Lagrange parameters by substitution. We then transform the problem to one of maximizing some functions of the cell probabilities simultaneously. We apply this problem to some real data sets, namely, a US Migration data, and a data on grading of unaided distance vision. We solve another estimation problem to determine the maximum likelihood estimation of the parameters of the latent variable models such as Bradley-Terry model where the data come from a paired comparisons experiment. We approach this problem by considering the observed frequency having a binomial distribution and then replacing the binomial parameters in terms of optimal design weights. We apply this problem to a data set from American League Baseball Teams.
Finally, we construct some optimal structure designs for comparing test treatments with a control. We introduce different structure designs and establish their properties using the incidence and characteristic matrices. We also develop methods of obtaining optimal R-type structure designs and show how such designs are trace, A- and MV-optimal. October 2016
Lan, C. Edward. VORSTAB, a computer program for calculating lateral-directional stability derivatives with vortex flow effect. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1985.
Iliff, Kenneth W. X-29A lateral-directional stability and control derivatives extracted from high-angle-of-attack flight data. [Washington, D.C.]: National Aeronautics and Space Administration, Office of Management, Scientific and Technical Information Program, 1996.
Iliff, Kenneth W. X-29A lateral-directional stability and control derivatives extracted from high-angle-of-attack flight data. [Washington, D.C.]: National Aeronautics and Space Administration, Office of Management, Scientific and Technical Information Program, 1996.
Iliff, Kenneth W. X-29A lateral-directional stability and control derivatives extracted from high-angle-of-attack flight data. [Washington, D.C]: National Aeronautics and Space Administration, Office of Management, Scientific and Technical Information Program Center, 1996.
Iliff, Kenneth W. X-29A lateral-directional stability and control derivatives extracted from high-angle-of-attack flight data. [Washington, D.C.]: National Aeronautics and Space Administration, Office of Management, Scientific and Technical Information Program, 1996.
Iliff, Kenneth W. X-29A lateral-directional stability and control derivatives extracted from high-angle-of-attack flight data. Washington, D.C: National Aeronautics and Space Administration, 1996.
Iliff, Kenneth W. Extraction of lateral-directional stability and control derivatives for the basic F-18 aircraft at high angles of attack. [Washington, D.C]: National Aeronautics and Space Administration, Office of Management, Scientific and Technical Information Program Center, 1997.
Iliff, Kenneth W. Extraction of lateral-directional stability and control derivatives for the basic F-18 aircraft at high angles of attack. [Washington, D.C.]: National Aeronautics and Space Administration, Office of Management, Scientific and Technical Information Program, 1997.
Iliff, Kenneth W. Extraction of lateral-directional stability and control derivatives for the basic F-18 aircraft at high angles of attack. [Washington, D.C.]: National Aeronautics and Space Administration, Office of Management, Scientific and Technical Information Program, 1997.
Book chapters on the topic "Directional derivatives":
1
Lipsman, Ronald L., and Jonathan M. Rosenberg. "Directional Derivatives." In Multivariable Calculus with MATLAB®, 75–94. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-65070-8_5.
Coombes, Kevin R., Ronald L. Lipsman, and Jonathan M. Rosenberg. "Directional Derivatives." In Multivariable Calculus and Mattiematica®, 81–102. New York, NY: Springer New York, 1998. http://dx.doi.org/10.1007/978-1-4612-1698-8_5.
Luderer, Bernd, Leonid Minchenko, and Tatyana Satsura. "Directional Derivatives of Marginal Functions." In Nonconvex Optimization and Its Applications, 77–96. Boston, MA: Springer US, 2002. http://dx.doi.org/10.1007/978-1-4757-3468-3_5.
Gilbert, Robert P., Michael Shoushani, and Yvonne Ou. "Directional Derivatives and Extremum Problems." In Multivariable Calculus with Mathematica, 117–77. Boca Raton : Chapman & Hall/CRC Press, 2020.: Chapman and Hall/CRC, 2020. http://dx.doi.org/10.1201/9781315161471-4.
Ward, D. "Convex Directional Derivatives in Optimization." In Generalized Convexity and Fractional Programming with Economic Applications, 36–51. Berlin, Heidelberg: Springer Berlin Heidelberg, 1990. http://dx.doi.org/10.1007/978-3-642-46709-7_4.
Mohamed, Majeed, and Vikalp Dongare. "Identification of Aircraft Lateral-Directional Derivatives." In Aircraft Aerodynamic Parameter Estimation from Flight Data Using Neural Partial Differentiation, 33–46. Singapore: Springer Singapore, 2021. http://dx.doi.org/10.1007/978-981-16-0104-0_4.
Elster, K. H., and J. Thierfelder. "On Cone Approximations and Generalized Directional Derivatives." In Nonsmooth Optimization and Related Topics, 133–54. Boston, MA: Springer US, 1989. http://dx.doi.org/10.1007/978-1-4757-6019-4_9.
Gaffke, N. "Singular Information Matrices, Directional Derivatives, and Subgradients in Optimal Design Theory." In Linear Statistical Inference, 61–77. New York, NY: Springer New York, 1985. http://dx.doi.org/10.1007/978-1-4615-7353-1_6.
Liu, Gaolian, Zhiqiang Ye, and Bo Chen. "A Variational Mesh-Free Method Based on Discretization via Directional Derivatives." In Computational Mechanics, 340. Berlin, Heidelberg: Springer Berlin Heidelberg, 2007. http://dx.doi.org/10.1007/978-3-540-75999-7_140.
Dentcheva, Darinka, Werner Römisch, and Rüdiger Schultz. "Strong Convexity and Directional Derivatives of Marginal Values in Two-Stage Stochastic Programming." In Lecture Notes in Economics and Mathematical Systems, 8–21. Berlin, Heidelberg: Springer Berlin Heidelberg, 1995. http://dx.doi.org/10.1007/978-3-642-88272-2_2.
Conference papers on the topic "Directional derivatives":
1
Sherstov, Alexander A. "Communication lower bounds using directional derivatives." In the 45th annual ACM symposium. New York, New York, USA: ACM Press, 2013. http://dx.doi.org/10.1145/2488608.2488725.
Zheng, Sheng, Jin Wen Tian, and Jian Liu. "Weighted MLS-SVM for approximation of directional derivatives." In MIPPR 2005 Image Analysis Techniques, edited by Deren Li and Hongchao Ma. SPIE, 2005. http://dx.doi.org/10.1117/12.655103.
Luna-Elizarrarás, M. E., M. A. Macías-Cedeño, M. Shapiro, Theodore E. Simos, George Psihoyios, and Ch Tsitouras. "On Relations between the Derivative and the Two-Dimensional Directional Derivatives of a Quaternionic Function." In Numerical Analysis and Applied Mathematics. AIP, 2007. http://dx.doi.org/10.1063/1.2790263.
F. Xu, X., Y. Y. Deng, and Z. X. He. "Application of Magnetic Directional Derivatives in Petroleum Geology Interpretation." In 69th EAGE Conference and Exhibition incorporating SPE EUROPEC 2007. European Association of Geoscientists & Engineers, 2007. http://dx.doi.org/10.3997/2214-4609.201401968.
Qian, Jiye, Hengjun Zhao, Jin Fu, Guojun He, Xingzhe Hou, Bin Fang, and Jide Qian. "No-reference image sharpness metric based on directional derivatives." In 2017 International Conference on Security, Pattern Analysis, and Cybernetics (SPAC). IEEE, 2017. http://dx.doi.org/10.1109/spac.2017.8304301.
Wu, Xiaogu, and William G. Wee. "Surface detection with subvoxel accuracy using 3D directional derivatives." In Nondestructive Evaluation Techniques for Aging Infrastructures & Manufacturing, edited by Ajit K. Mal. SPIE, 1999. http://dx.doi.org/10.1117/12.339907.
Escalante-Ramirez, Boris, and Jose L. Silvan-Cardenas. "Multiresolution directional-oriented image transform based on Gaussian derivatives." In International Symposium on Optical Science and Technology, edited by Andrew F. Laine, Michael A. Unser, and Akram Aldroubi. SPIE, 2001. http://dx.doi.org/10.1117/12.449717.
Legarda-Saenz, Ricardo. "Fast wavefront estimation using multiple directional derivatives and quadrature transform." In Ninth International Symposium on Laser Metrology, edited by Chenggen Quan and Anand Asundi. SPIE, 2008. http://dx.doi.org/10.1117/12.814611.
Legarda-Saenz, Ricardo. "Robust wavefront reconstruction using multiple directional derivatives and computer monitor." In Sixth Symposium Optics in Industry, edited by Julio C. Gutiérrez-Vega, Josué Dávila-Rodríguez, and Carlos López-Mariscal. SPIE, 2007. http://dx.doi.org/10.1117/12.742643.
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Ostashev, Vladimir, Michael Muhlestein, and D. Wilson. Extra-wide-angle parabolic equations in motionless and moving media. Engineer Research and Development Center (U.S.), September 2021. http://dx.doi.org/10.21079/11681/42043.
Wide-angle parabolic equations (WAPEs) play an important role in physics. They are derived by an expansion of a square-root pseudo-differential operator in one-way wave equations, and then solved by finite-difference techniques. In the present paper, a different approach is suggested. The starting point is an extra-wide-angle parabolic equation (EWAPE) valid for small variations of the refractive index of a medium. This equation is written in an integral form, solved by a perturbation technique, and transformed to the spectral domain. The resulting split-step spectral algorithm for the EWAPE accounts for the propagation angles up to 90° with respect to the nominal direction. This EWAPE is also generalized to large variations in the refractive index. It is shown that WAPEs known in the literature are particular cases of the two EWAPEs. This provides an alternative derivation of the WAPEs, enables a better understanding of the underlying physics and ranges of their applicability, and opens an opportunity for innovative algorithms. Sound propagation in both motionless and moving media is considered. The split-step spectral algorithm is particularly useful in the latter case since complicated partial derivatives of the sound pressure and medium velocity reduce to wave vectors (essentially, propagation angles) in the spectral domain.
