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Articoli di riviste sul tema "Formulation Inverse"

Autore: Grafiati

Pubblicato: 31 agosto 2024

Ultima modifica: 10 luglio 2025

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1

Faroughi, S., and H. Ahmadian. "Shape functions associated with inverse element formulations." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 225, no. 2 (2010): 304–11. http://dx.doi.org/10.1243/09544062jmes2350.

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Super-convergent element formulations in local co-ordinates are obtained using inverse strategies. In the inverse approach discretization errors of the element formulation are minimized leading to super-convergent solutions. In the development of the inverse element model, no shape functions are introduced and therefore the task of element transformation from local to global co-ordinates system remains a challenge. In this paper, a procedure is proposed to produce shape functions associated with the inverse element formulations via hierarchical polynomials. A membrane element formulation is developed using inverse strategy as an example and its associated shape functions are determined using hierarchical polynomials. Numerical results indicate higher accuracy of the developed model in global co-ordinates compared to the reported models in the literature for the same element.

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2

Vitoshkin, H., and A. Yu Gelfgat. "On Direct and Semi-Direct Inverse of Stokes, Helmholtz and Laplacian Operators in View of Time-Stepper-Based Newton and Arnoldi Solvers in Incompressible CFD." Communications in Computational Physics 14, no. 4 (2013): 1103–19. http://dx.doi.org/10.4208/cicp.300412.010213a.

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AbstractFactorization of the incompressible Stokes operator linking pressure and velocity is revisited. The main purpose is to use the inverse of the Stokes operator with a large time step as a preconditioner for Newton and Arnoldi iterations applied to computation of steady three-dimensional flows and study of their stability. It is shown that the Stokes operator can be inversed within an acceptable computational effort. This inverse includes fast direct inverses of several Helmholtz operators and iterative inverse of the pressure matrix. It is shown, additionally, that fast direct solvers can be attractive for the inverse of the Helmholtz and Laplace operators on fine grids and at large Reynolds numbers, as well as for other problems where convergence of iterative methods slows down. Implementation of the Stokes operator inverse to time-stepping-based formulation of the Newton and Arnoldi iterations is discussed.

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3

Guritman, Sugi, Jaharuddin, Teduh Wulandari Mas'oed, and Siswandi. "A FAST COMPUTATION FOR EIGENVALUES OF CIRCULANT MATRICES WITH ARITHMETIC SEQUENCE." MILANG Journal of Mathematics and Its Applications 19, no. 1 (2023): 69–80. http://dx.doi.org/10.29244/milang.19.1.69-80.

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In this article, we derive simple formulations of the eigenvalues, determinants, and also the inverse of circulant matrices whose entries in the first row form an arithmetic sequence. The formulation of the determinant and inverse is based on elementary row and column operations transforming the matrix to an equivalent diagonal matrix so that the formulation is obtained easily. Meanwhile, for the eigenvalues formulation, we simplify the known result of formulation for the general circulant matrices by exploiting the properties of the cyclic group induced by the set of all roots of as the set of points in the unit circle in the complex plane, and also by considering the specific property of arithmetic sequence. Then, we construct an algorithm for the eigenvalues formulation. This algorithm shows a better computation compared to the previously known result for the general case of circulant matrices.

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4

Kono, Masaru, and Hideo Uchimura. "Inverse Problem of Paleomagnetic Reconstruction: Formulation." Journal of geomagnetism and geoelectricity 46, no. 4 (1994): 311–28. http://dx.doi.org/10.5636/jgg.46.311.

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5

Zeng, Xiaogang, and Sunil Saigal. "An Inverse Formulation With Boundary Elements." Journal of Applied Mechanics 59, no. 4 (1992): 835–40. http://dx.doi.org/10.1115/1.2894050.

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A mathematical formulation for the solution of inverse problems pertaining to the identification of flaw shapes and the reconstruction of boundary conditions in a continua is described. Integral relationships are derived for the variation of field variables with respect to variation in flaw shape using Taylor series expansions. Similar relationships for the variation of boundary conditions with variation inflow shape are also obtained. These variations allow the development of an iterative framework to advance an initially assumed flaw shape towards its actual configuration. The iterations are based upon and are driven by the difference in the values of computed response for the assumed flaw shape from their experimentally measured values at specified locations. The resulting equations are cast into the matrix form for solution using the boundary element method.

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6

Yagle, Andrew E. "Multidimensional inverse scattering: An orthogonalization formulation." Journal of Mathematical Physics 28, no. 7 (1987): 1481–91. http://dx.doi.org/10.1063/1.527503.

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7

Li, Jiwei, Lingyun Qiu, Zhongjing Wang, and Hui Yu. "Flow Measurement: An Inverse Problem Formulation." SIAM Journal on Applied Mathematics 83, no. 4 (2023): 1654–76. http://dx.doi.org/10.1137/22m1530720.

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8

CYRIL, X., J. ANGELES, and A. MISRA. "EFFICIENT INVERSE DYNAMICS OF GENERAL N-AXIS ROBOTIC MANIPULATORS." Transactions of the Canadian Society for Mechanical Engineering 13, no. 4 (1989): 91–95. http://dx.doi.org/10.1139/tcsme-1989-0015.

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Presented in this paper is an efficient scheme to solve the inverse dynamics problem associated with robotic manipulators of arbitrary architecture, using the recursive Newton-Euler formulation. The scheme’s efficiency derives from the use of suitable coordinate frame to represent the vector quantities and the suitable manipulation of the vector operations. The computational complexities of this and other general dynamical formulations published so far are compared. In conclusion, it is observed that not only the dynamical formulation methodology, but also the judicious representation and manipulation of the vector quantities contribute to the computational efficiency of the algorithm. An example is presented to show the validity of the computational scheme.

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9

Duplij, Steven. "Higher Regularity, Inverse and Polyadic Semigroups." Universe 7, no. 10 (2021): 379. http://dx.doi.org/10.3390/universe7100379.

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We generalize the regularity concept for semigroups in two ways simultaneously: to higher regularity and to higher arity. We show that the one-relational and multi-relational formulations of higher regularity do not coincide, and each element has several inverses. The higher idempotents are introduced, and their commutation leads to unique inverses in the multi-relational formulation, and then further to the higher inverse semigroups. For polyadic semigroups we introduce several types of higher regularity which satisfy the arity invariance principle as introduced: the expressions should not depend of the numerical arity values, which allows us to provide natural and correct binary limits. In the first definition no idempotents can be defined, analogously to the binary semigroups, and therefore the uniqueness of inverses can be governed by shifts. In the second definition called sandwich higher regularity, we are able to introduce the higher polyadic idempotents, but their commutation does not provide uniqueness of inverses, because of the middle terms in the higher polyadic regularity conditions. Finally, we introduce the sandwich higher polyadic regularity with generalized idempotents.

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10

Guritman, Sugi, Jaharuddin, Teduh Wulandari, and Siswandi. "An Efficient Method for Computing the Inverse and Eigenvalues of Circulant Matrices with Lucas Numbers." Journal of Advances in Mathematics and Computer Science 39, no. 4 (2024): 10–23. http://dx.doi.org/10.9734/jamcs/2024/v39i41879.

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In this article, the inverse including the determinant, and the eigenvalues of circulant matrices with entry Lucas numbers are formulated explicitly in a simple way so that their computations can be constructed efficiently. The formulation method of the determinant and inverse is simply applying the theory of elementary row or column operations and can be unified in one theorem. Meanwhile, for the eigenvalues formulation, the recently known formulation in the case of general circulant matrices is simplified by observing the specialty of the Lucas sequence and applying cyclic group properties of unit circles in the complex plane. Then, an algorithm of those formulations is constructed efficiently. From some implementation facts also showed that the algorithms performed very fast and was able to calculate large size of circulant matrices.

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11

Khan, Waseem A., Venkat N. Krovi, Subir K. Saha, and Jorge Angeles. "Recursive Kinematics and Inverse Dynamics for a Planar 3R Parallel Manipulator." Journal of Dynamic Systems, Measurement, and Control 127, no. 4 (2004): 529–36. http://dx.doi.org/10.1115/1.2098890.

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We focus on the development of modular and recursive formulations for the inverse dynamics of parallel architecture manipulators in this paper. The modular formulation of mathematical models is attractive especially when existing sub-models may be assembled to create different topologies, e.g., cooperative robotic systems. Recursive algorithms are desirable from the viewpoint of simplicity and uniformity of computation. However, the prominent features of parallel architecture manipulators-the multiple closed kinematic loops, varying locations of actuation together with mixtures of active and passive joints-have traditionally hindered the formulation of modular and recursive algorithms. In this paper, the concept of the decoupled natural orthogonal complement (DeNOC) is combined with the spatial parallelism of the robots of interest to develop an inverse dynamics algorithm which is both recursive and modular. The various formulation stages in this process are highlighted using the illustrative example of a 3R Planar Parallel Manipulator.

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12

Cotter, C. J., D. D. Holm, and P. E. Hydon. "Multisymplectic formulation of fluid dynamics using the inverse map." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 463, no. 2086 (2007): 2671–87. http://dx.doi.org/10.1098/rspa.2007.1892.

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We construct multisymplectic formulations of fluid dynamics using the inverse of the Lagrangian path map. This inverse map, the ‘back-to-labels’ map, gives the initial Lagrangian label of the fluid particle that currently occupies each Eulerian position. Explicitly enforcing the condition that the fluid particles carry their labels with the flow in Hamilton's principle leads to our multisymplectic formulation. We use the multisymplectic one-form to obtain conservation laws for energy, momentum and an infinite set of conservation laws arising from the particle relabelling symmetry and leading to Kelvin's circulation theorem. We discuss how multisymplectic numerical integrators naturally arise in this approach.

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13

Peidro, Adrian, and Edward J. Haug. "Obstacle Avoidance in Operational Configuration Space Kinematic Control of Redundant Serial Manipulators." Machines 12, no. 1 (2023): 10. http://dx.doi.org/10.3390/machines12010010.

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Kinematic control of redundant serial manipulators has been carried out for the past half century based primarily on a generalized inverse velocity formulation that is known to have mathematical deficiencies. A recently developed inverse kinematic configuration mapping is employed in an operational configuration space differentiable manifold formulation for redundant-manipulator kinematic control with obstacle avoidance. This formulation is shown to resolve deficiencies in the generalized inverse velocity formulation, especially for high-degree-of-redundancy manipulators. Tracking a specified output trajectory while avoiding obstacles for four- and twenty-degree-of-redundancy manipulators is carried out to demonstrate the effectiveness of the differentiable manifold approach for applications with a high degree of redundancy and to show that it indeed resolves deficiencies of the conventional generalized inverse velocity formulation in challenging applications.

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14

Vasco, D. W. "An algebraic formulation of geophysical inverse problems." Geophysical Journal International 142, no. 3 (2000): 970–90. http://dx.doi.org/10.1046/j.1365-246x.2000.00188.x.

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15

Nowack, Robert L. "Tomography and the Herglotz-Wiechert inverse formulation." Pure and Applied Geophysics PAGEOPH 133, no. 2 (1990): 305–15. http://dx.doi.org/10.1007/bf00877165.

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16

Manurung, Andrew Bony Nabasar, Siti Nurrohmah, and Ida Fithriani. "Formulation of Kumaraswamy Generalized Inverse Lomax Distribution." Proceedings of The International Conference on Data Science and Official Statistics 2023, no. 1 (2023): 737–44. http://dx.doi.org/10.34123/icdsos.v2023i1.416.

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Lifetime data is a type of data that consists of a waiting time until an event occurs and modelled by numerous distributions. One of its characteristics that is interesting to be studied is the hazard function due to the flexibility that it has compared to other characteristics of distribution. Inverse Lomax (IL) distribution is one of the distributions considered to have advantages in modelling hazard shape and extended in several ways to address the problem of non-monotone hazard which is often encountered in real life data. However, it needs to be extended to another family of distribution to increase its modelling potential and Kumaraswamy Generalized (KG) family of distribution is used as it adds two more parameters to the distribution. The newly developed distribution is called the Kumaraswamy Generalized Inverse Lomax (KGIL) distribution. The main characteristics of KGIL distribution will be derived, such as cumulative distribution function (cdf), probability density function (pdf), hazard function, and survival function. Maximum likelihood method will also be used to estimate the parameters. The application of the new model is based on head-and-neck cancer lifetime data set. The modelling results show that the KGIL distribution is the best to capture important details of the data set considered

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17

Germain, Sandrine, and Paul Steinmann. "Towards Inverse Form Finding Methods for a Deep Drawing Steel DC04." Key Engineering Materials 504-506 (February 2012): 619–24. http://dx.doi.org/10.4028/www.scientific.net/kem.504-506.619.

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A challenge in the design of functional parts in metal forming processes is the determination of the initial, undeformed shape such that under a given load a part will obtain the desired deformed shape. An inverse mechanical or a shape optimization formulation might be used to solve this problem, which is inverse to the standard kinematic analysis in which the undeformed shape is known and the deformed shape unknown. The objective of the inverse mechanical formulation aims in the inverse deformation map that determines the (undeformed) material configuration, where the spatial (deformed) configuration and the mechanical loads are given. The shape optimization formulation predicts the initial shape in the sense of an inverse problem via successive iterations of the direct problem. In this paper, both methods are presented using a formulation in the logarithmic strain space. An update of the reference configuration of the sheet of metal during the optimization process is proposed in order to avoid mesh distortions. A first example showed the results obtained with both methods in isotropic hyperelasticity. A second example illustrated a simplified deep drawing computed with the shape optimization formulation in isotropic elastoplasticity. From the undeformed shapes obtained with both methods the deformed shapes are acquired with the direct mechanical formulation. Compared to the target deformed shape a minor difference in node coordinates is found. The computation time is lower with the inverse mechanical formulation in hyperelasticity. The update of the reference configuration in the shape optimization formulation allowed to avoid mesh distortions but increased the computational costs.

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18

Prasanna, Parvathy, Jeevamma Jacob, and Mattida Ponnadiyil Nandakumar. "Inverse optimal control of a class of affine nonlinear systems." Transactions of the Institute of Measurement and Control 41, no. 9 (2019): 2637–50. http://dx.doi.org/10.1177/0142331218806338.

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This paper proposes a systematic formulation of inverse optimal control (IOC) law based on a rather straightforward reduction of control Lyapunov function (CLF), applicable to a class of second-order nonlinear systems affine in the input. This method exploits the additional design degrees of freedom resulting from the non-uniqueness of the state dependent coefficient (SDC) formulation, which is widely used in pseudo-linear control techniques. The applicability of the proposed approach necessitates an apparently effortless SDC formulation satisfying an SDC matrix criterion in terms of the structure and characteristics of the state matrix, [Formula: see text]. Subsequently, a sufficient condition for the global asymptotic stability (g.a.s) of the closed-loop system is established. The SDC formulations conforming to the sufficient condition ensure the existence and determination of a smooth radially unbounded polynomial CLF of the form [Formula: see text], while offering a benevolent choice for the gain matrix [Formula: see text], in the CLF. The direct relationship between the gain matrix [Formula: see text] and state weighing matrix [Formula: see text] ensures optimization of an equivalent [Formula: see text]. This feature enables one to rightfully choose the gain matrix [Formula: see text] as per the performance requisites of the system. Finally, the application of the proposed methodology for the speed control of a permanent magnet synchronous motor validates the efficacy and design flexibility of the methodology.

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19

CHUNG, B. K., K. G. JOO, and SOONKEON NAM. "HAMILTONIAN FORMULATION OF SL(3) Ur-KdV EQUATION." Modern Physics Letters A 08, no. 31 (1993): 2927–36. http://dx.doi.org/10.1142/s0217732393003342.

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We give a unified view of the relation between the SL(2) KdV, the mKdV, and the Ur-KdV equations through the Fréchet derivatives and their inverses. For this we introduce a new procedure of obtaining the Ur-KdV equation, where we require that it has no nonlocal operators. We extend this method to the SL(3) KdV equation, i.e. Boussinesq (Bsq) equation and obtain the Hamiltonian structure of Ur-Bsq .equation in a simple form. In particular, we explicitly construct the Hamiltonian operator of the Ur-Bsq system which defines the Poisson structure of the system, through the Fréchet derivative and its inverse.

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20

Liu, Hui, and Li Wen Guan. "Dynamic Modeling of a High-Dynamic Flight Simulator." Applied Mechanics and Materials 687-691 (November 2014): 610–15. http://dx.doi.org/10.4028/www.scientific.net/amm.687-691.610.

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High-dynamic flight simulator (HDFS), using a centrifuge as its motion base, is a machine utilized for simulating the acceleration environment associated with modern advanced tactical aircrafts. This paper models the HDFS as a robotic system with three rotational degrees of freedom. The forward and inverse dynamic formulations are carried out by the recursive Newton-Euler approach. The driving torques acting on the joints are determined on the basis of the inverse dynamic formulation. The formulation has been implemented in two numerical simulation examples, which are used for calculating the maximum torques of actuators and simulating the time-histories of kinematic and dynamic parameters of pure trapezoid Gz-load command profiles, respectively. The simulation results can be applied to the design of the control system. The dynamic modeling approach presented in this paper can also be generalized to some similar devices.

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21

Igarashi, Gaku, and Yoshihide Kakizawa. "Re-formulation of inverse Gaussian, reciprocal inverse Gaussian, and Birnbaum–Saunders kernel estimators." Statistics & Probability Letters 84 (January 2014): 235–46. http://dx.doi.org/10.1016/j.spl.2013.10.013.

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22

Frankel, J. I., H. C. Chen, and M. Keyhani. "New Step Response Formulation for Inverse Heat Conduction." Journal of Thermophysics and Heat Transfer 31, no. 4 (2017): 989–96. http://dx.doi.org/10.2514/1.t5067.

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23

UCHODA, Kazuo, and Kazuonori HASE. "Simple Formulation for Inverse Dynamics Satisfying Kinetic Consistency." Proceedings of the Symposium on sports and human dynamics 2020 (2020): A—7–3. http://dx.doi.org/10.1299/jsmeshd.2020.a-7-3.

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Leal, Allan M. M., and William R. Smith. "Inverse chemical equilibrium problems: General formulation and algorithm." Chemical Engineering Science 252 (April 2022): 117162. http://dx.doi.org/10.1016/j.ces.2021.117162.

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25

Chaux, Caroline, Patrick L. Combettes, Jean-Christophe Pesquet, and Valérie R. Wajs. "A variational formulation for frame-based inverse problems." Inverse Problems 23, no. 4 (2007): 1495–518. http://dx.doi.org/10.1088/0266-5611/23/4/008.

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26

Puel, G., and D. Aubry. "Two-time-scale inverse problems: formulation and solution." Journal of Physics: Conference Series 657 (November 16, 2015): 012005. http://dx.doi.org/10.1088/1742-6596/657/1/012005.

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27

Blok, H., and M. C. S. Zeylmans. "Reciprocity and the formulation of inverse profiling problems." Radio Science 22, no. 7 (1987): 1137–47. http://dx.doi.org/10.1029/rs022i007p01137.

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28

Baranov, V. I., and L. A. Gribov. "Formulation and solution of the inverse vibronic problem." Journal of Applied Spectroscopy 51, no. 1 (1989): 700–704. http://dx.doi.org/10.1007/bf00664372.

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29

Dey, Arindam, and Prabir Basudhar. "Estimation of Burger model parameters using inverse formulation." International Journal of Geotechnical Engineering 6, no. 3 (2012): 261–74. http://dx.doi.org/10.3328/ijge.2012.06.03.261-274.

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30

YOSHIMURA, TOSHIO, and KAZUSHIGE IKUTA. "Inverse heat-conduction problem by finite-element formulation." International Journal of Systems Science 16, no. 11 (1985): 1365–75. http://dx.doi.org/10.1080/00207728508926757.

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31

UCHIDA, Kazuo, and Kazunori HASE. "Simple formulation for inverse dynamics satisfying kinetic consistency." Proceedings of the Dynamics & Design Conference 2016 (2016): 401. http://dx.doi.org/10.1299/jsmedmc.2016.401.

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Frankel, J. I., and M. Keyhani. "Response function formulation for inverse heat conduction: concept." Journal of Engineering Mathematics 110, no. 1 (2017): 75–95. http://dx.doi.org/10.1007/s10665-017-9932-8.

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Zhou, Xianlian, and Jia Lu. "Inverse formulation for geometrically exact stress resultant shells." International Journal for Numerical Methods in Engineering 74, no. 8 (2008): 1278–302. http://dx.doi.org/10.1002/nme.2215.

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34

Masson, Philippe Le, and Helcio R. B. Orlande. "Thermophysical characterization of materials at high temperatures by solving inverse problems within the Bayesian framework of statistics." High Temperatures-High Pressures 50, no. 2 (2021): 77–104. http://dx.doi.org/10.32908/hthp.v50.973.

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Inverse heat transfer problems deal with the estimation of parameters or functions appearing in the mathematical formulation of problems in thermal sciences, by utilizing measurements of dependent variables of the formulation. Inverse problems are extremely useful for the indirect measurement of thermophysical properties, in particular for challenging situations involving high temperatures, where coupled multi-physics phenomena and nonlinearities must be taken into account. In this paper, basic inverse problem concepts are reviewed. Solution techniques within the Bayesian framework of statistics are briefly described and applied to two inverse problems related to the authors� experience on the estimation of thermophysical properties at high temperatures.

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Penenko, A. V., V. S. Konopleva, and V. V. Penenko. "Inverse modeling of atmospheric chemistry with a differential evolution solver: Inverse problem and Data assimilation." IOP Conference Series: Earth and Environmental Science 1023, no. 1 (2022): 012015. http://dx.doi.org/10.1088/1755-1315/1023/1/012015.

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Abstract In this paper, we numerically compare an inverse problem for an atmospheric chemistry model, when all the measurement data is available a priory, to a corresponding data assimilation problem when the data are obtained in some portions during the simulation. In both cases, we reconstruct the unobservable parts of the model state function by the observable ones (i.e., solve a continuation problem). This is done by identifying the model reaction rate parameters with the available measurement data by solving an optimization problem with a derivative-free differential evolution solver. In our numerical experiments, the inverse problem formulation of the continuation problem has not necessarily provided better results than the data assimilation formulation despite the latter being more limited in the measurement data.

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Dong, Jinlong, Luca Di Rienzo, Olivier Chadebec, and Jianhua Wang. "Application of Whitney elements for the reconstruction of electric arc current density in low-voltage circuit breakers." COMPEL - The international journal for computation and mathematics in electrical and electronic engineering 38, no. 3 (2019): 1036–47. http://dx.doi.org/10.1108/compel-09-2018-0359.

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Purpose This paper aims to present the mathematical formulations of a magnetic inverse problem for the electric arc current density reconstruction in a simplified arc chamber of a low-voltage circuit breaker. Design/methodology/approach Considering that electric arc current density is a zero divergence vector field, the inverse problem can be solved in Whitney space W2 in terms of electric current density J with the zero divergence condition as a constraint or can be solved in Whitney space W1 in terms of electric vector potential T where the zero divergence condition naturally holds. Moreover, the tree gauging condition is applied to ensure a unique solution when solving for the vector potential in space W1. Tikhonov regularization is used to treat the ill-posedness of the inverse problem complemented with L-curve method for the selection of regularization parameters. A common mode approach is proposed, which solves for the reduced electric vector potential representing the internal current loops instead of solving for the total electric vector potential. The proposed inversion approaches are numerically tested starting from simulated magnetic field values. Findings With the common mode approach, the reconstruction of current density is significantly improved for both formulations using face elements in space W2 and using edge elements in space W1. When solving the inverse problem in space W1, the choice of the regularization operator has a key role to obtain a good reconstruction, where the discrete curl operator is a good option. The standard Tikhonov regularization obtains a good reconstruction with J-formulation, but fails in the case of T-formulation. The use of edge elements requires a tree-cotree gauging to ensure the uniqueness of T. Moreover, additional efforts have to be taken to find an optimal regularization operator and an optimal tree when using edge elements. In conclusion, the J-formulation is to be preferred. Originality/value The proposed approaches are able to reconstruct the three-dimensional electric arc current density from its magnetic field in a non-intrusive manner. The formulations enable us to incorporate a priori knowledge of the unknown current density into the solution of the inverse problem, including the zero divergence condition and the boundary conditions. A common mode approach is proposed, which can significantly improve the current density reconstruction.

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Sariyildiz, Emre, Eray Cakiray, and Hakan Temeltas. "A Comparative Study of Three Inverse Kinematic Methods of Serial Industrial Robot Manipulators in the Screw Theory Framework." International Journal of Advanced Robotic Systems 8, no. 5 (2011): 64. http://dx.doi.org/10.5772/45696.

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In this paper, we compare three inverse kinematic formulation methods for the serial industrial robot manipulators. All formulation methods are based on screw theory. Screw theory is an effective way to establish a global description of rigid body and avoids singularities due to the use of the local coordinates. In these three formulation methods, the first one is based on quaternion algebra, the second one is based on dual-quaternions, and the last one that is called exponential mapping method is based on matrix algebra. Compared with the matrix algebra, quaternion algebra based solutions are more computationally efficient and they need less storage area. The method which is based on dual-quaternion gives the most compact and computationally efficient solution. Paden-Kahan sub-problems are used to derive inverse kinematic solutions. 6-DOF industrial robot manipulator's forward and inverse kinematic equations are derived using these formulation methods. Simulation and experimental results are given.

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Aliatiningtyas, Nur, Sugi Guritman, and Teduh Wulandari. "On the Explicit Formula for Eigenvalues, Determinant, and Inverse of Circulant Matrices." JTAM (Jurnal Teori dan Aplikasi Matematika) 6, no. 3 (2022): 711. http://dx.doi.org/10.31764/jtam.v6i3.8616.

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Determining eigenvalues, determinants, and inverse for a general matrix is computationally hard work, especially when the size of the matrix is large enough. But, if the matrix has a special type of entry, then there is an opportunity to make it much easier by giving its explicit formulation. In this article, we derive explicit formulas for determining eigenvalues, determinants, and inverses of circulant matrices with entries in the first row of those matrices in any formation of a sequence of numbers. The main method of our study is exploiting the circulant property of the matrix and associating it with cyclic group theory to get the results of the formulation. In every discussion of those concepts, we also present some computation remarks.

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SISWANDI, SISWANDI, SUGI GURITMAN, NUR ALIATININGTYAS, and TEDUH WULANDARI. "A COMPUTATION PERSPECTIVE FOR THE EIGENVALUES OF CIRCULANT MATRICES INVOLVING GEOMETRIC PROGRESSION." Jurnal Matematika UNAND 12, no. 1 (2023): 65. http://dx.doi.org/10.25077/jmua.12.1.65-77.2023.

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In this article, the eigenvalues and inverse of circulant matrices with entries in the first row having the form of a geometric sequence are formulated explicitly in a simple form in one theorem. The method for deriving the formulation of the determinant and inverse is simply using elementary row or column operations. For the eigenvalues, the known formulation of the previous results is simplified by considering the specialty of the sequence and using cyclic group properties of unit circles in the complex plane. Then, the algorithm of eigenvalues formulation is constructed, and it shows as a better computation method.

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40

Steen-Larsen, Hans Christian, Edwin D. Waddington, and Michelle R. Koutnik. "Formulating an inverse problem to infer the accumulation-rate pattern from deep internal layering in an ice sheet using a Monte Carlo approach." Journal of Glaciology 56, no. 196 (2010): 318–32. http://dx.doi.org/10.3189/002214310791968476.

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AbstractUsing a Monte Carlo (MC) method, we determine the accumulation-rate profile along a flowband, the influx of ice into the upstream end of the flowband and the age of an internal layer. The data comprise the depth profile of the internal layer, a few velocity measurements at the surface and the average accumulation at one location. The data in our example were collected at Taylor Mouth, a flank site off Taylor Dome, Antarctica. We present three alternative formulations of this inverse problem. Depending on the formulation used, this particular inverse problem can have up to four solutions, each corresponding to a different spatial accumulation-rate pattern. This study demonstrates the ability of a MC method to find several solutions to this inverse problem, and how to use a Metropolis algorithm to determine the probability distribution of each of these different solutions. The only disadvantage of the MC method is that it is computationally more expensive than other inverse methods, such as the Gradient method.

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41

Xie, Shunqing. "Inverse dynamic formulation of a novel hybrid machine tool." Chinese Journal of Mechanical Engineering (English Edition) 16, no. 02 (2003): 184. http://dx.doi.org/10.3901/cjme.2003.02.184.

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42

Volpe, Ernani V., Guilherme L. Oliveira, Luis C. C. Santos, Marcelo T. Hayashi, and Marco A. B. Ceze. "Inverse aerodynamic design applications using the MGM hybrid formulation." Inverse Problems in Science and Engineering 17, no. 2 (2009): 245–61. http://dx.doi.org/10.1080/17415970802083615.

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Manca, Vincenzo, and Luca Marchetti. "An algebraic formulation of inverse problems in MP dynamics." International Journal of Computer Mathematics 90, no. 4 (2013): 845–56. http://dx.doi.org/10.1080/00207160.2012.735362.

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Sten, Johan C. E., and Edwin A. Marengo. "Inverse Source Problem in the Spheroidal Geometry: Vector Formulation." IEEE Transactions on Antennas and Propagation 56, no. 4 (2008): 961–69. http://dx.doi.org/10.1109/tap.2008.919176.

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Vatul’yan, A. O. "Variational formulation of inverse coefficient problems for elastic bodies." Doklady Physics 53, no. 9 (2008): 497–99. http://dx.doi.org/10.1134/s1028335808090085.

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Paradiso, Sean P., Kris T. Delaney, and Glenn H. Fredrickson. "Swarm Intelligence Platform for Multiblock Polymer Inverse Formulation Design." ACS Macro Letters 5, no. 8 (2016): 972–76. http://dx.doi.org/10.1021/acsmacrolett.6b00494.

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47

Marks, Daniel L., and David R. Smith. "Inverse scattering with a non self-adjoint variational formulation." Optics Express 26, no. 6 (2018): 7655. http://dx.doi.org/10.1364/oe.26.007655.

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Manservisi, S., and M. Gunzburger. "A variational inequality formulation of an inverse elasticity problem." Applied Numerical Mathematics 34, no. 1 (2000): 99–126. http://dx.doi.org/10.1016/s0168-9274(99)00042-2.

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Hong, Wei. "Inverse Lagrangian formulation for the deformation of hyperelastic solids." Extreme Mechanics Letters 9 (December 2016): 30–39. http://dx.doi.org/10.1016/j.eml.2016.04.009.

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Blajer, Wojciech, and Krzysztof Kołodziejczyk. "Improved DAE formulation for inverse dynamics simulation of cranes." Multibody System Dynamics 25, no. 2 (2010): 131–43. http://dx.doi.org/10.1007/s11044-010-9227-6.

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