Journal articles: 'Inverse solution'

1

Constales, D., and J. Kačur. "On the solution of some inverse problems in infiltration." Mathematica Bohemica 126, no. 2 (2001): 307–22. http://dx.doi.org/10.21136/mb.2001.134025.

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Nikuie, M., and M. Z. Ahmad. "Minimal Solution of Singular LR Fuzzy Linear Systems." Scientific World Journal 2014 (2014): 1–7. http://dx.doi.org/10.1155/2014/517218.

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In this paper, the singular LR fuzzy linear system is introduced. Such systems are divided into two parts: singular consistent LR fuzzy linear systems and singular inconsistent LR fuzzy linear systems. The capability of the generalized inverses such as Drazin inverse, pseudoinverse, and {1}-inverse in finding minimal solution of singular consistent LR fuzzy linear systems is investigated.

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3

Zhou, Mengmeng, Jianlong Chen, and Néstor Thome. "The W-weighted Drazin-star matrix and its dual." Electronic Journal of Linear Algebra 37, no. 37 (February 3, 2021): 72–87. http://dx.doi.org/10.13001/ela.2021.5389.

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After decades studying extensively two generalized inverses, namely Moore--Penrose inverse and Drazin inverse, currently, we found immersed in a new generation of generalized inverses (core inverse, DMP inverse, etc.). The main aim of this paper is to introduce and investigate a matrix related to these new generalized inverses defined for rectangular matrices. We apply our results to the solution of linear systems.

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4

Chrastina, Jan. "Solution of the inverse problem of the calculus of variations." Mathematica Bohemica 119, no. 2 (1994): 157–201. http://dx.doi.org/10.21136/mb.1994.126079.

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DEIS, TIMOTHY, JOHN MEAKIN, and G. SÉNIZERGUES. "EQUATIONS IN FREE INVERSE MONOIDS." International Journal of Algebra and Computation 17, no. 04 (June 2007): 761–95. http://dx.doi.org/10.1142/s0218196707003755.

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It is known that the problem of determining consistency of a finite system of equations in a free group or a free monoid is decidable, but the corresponding problem for systems of equations in a free inverse monoid of rank at least two is undecidable. Any solution to a system of equations in a free inverse monoid induces a solution to the corresponding system of equations in the associated free group in an obvious way, but solutions to systems of equations in free groups do not necessarily lift to solutions in free inverse monoids. In this paper, we show that the problem of determining whether a solution to a finite system of equations in a free group can be extended to a solution of the corresponding system in the associated free inverse monoid is decidable. We are able to use this to solve the consistency problem for certain classes of single-variable equations in free inverse monoids.

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Wu, Yan, Li Hui Cheng, Guo Feng Fan, and Cai Dong Wang. "Inverse Kinematics Solution and Optimization of 6DOF Handling Robot." Applied Mechanics and Materials 635-637 (September 2014): 1355–59. http://dx.doi.org/10.4028/www.scientific.net/amm.635-637.1355.

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The kinematics equation of the handling robot with six free degrees has multiple sets inverse solution, and the robot system only can choose one optimized solutions to drive the robot to work. The kinematics model of the robot is established by D-H method, and the inverse solution is derived by an algebraic method. The best flexibility principle was introduced to determine a set of optimal solutions from 8 sets of feasible solutions. The correctness of robot inverse solution method is verified through a set of calculation examples.

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Erem, Burak, Alireza Ghodrati, Gilead Tadmor, Robert MacLeod, and Dana Brooks. "Combining initialization and solution inverse methods for inverse electrocardiography." Journal of Electrocardiology 44, no. 2 (March 2011): e21. http://dx.doi.org/10.1016/j.jelectrocard.2010.12.059.

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8

Zhong, Jin, and Yilin Zhang. "Dual group inverses of dual matrices and their applications in solving systems of linear dual equations." AIMS Mathematics 7, no. 5 (2022): 7606–24. http://dx.doi.org/10.3934/math.2022427.

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<abstract><p>In this paper, we study a kind of dual generalized inverses of dual matrices, which is called the dual group inverse. Some necessary and sufficient conditions for a dual matrix to have the dual group inverse are given. If one of these conditions is satisfied, then compact formulas and efficient methods for the computation of the dual group inverse are given. Moreover, the results of the dual group inverse are applied to solve systems of linear dual equations. The dual group-inverse solution of systems of linear dual equations is introduced. The dual analog of the real least-squares solution and minimal $ P $-norm least-squares solution are obtained. Some numerical examples are provided to illustrate the results obtained.</p></abstract>

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9

Sugihara, Tomomichi. "Numerical Solution of Inverse Kinematics." Journal of the Robotics Society of Japan 34, no. 3 (2016): 167–73. http://dx.doi.org/10.7210/jrsj.34.167.

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10

Hald, O. H., and J. R. McLaughlin. "Solution of inverse nodal problems." Inverse Problems 5, no. 3 (June 1, 1989): 307–47. http://dx.doi.org/10.1088/0266-5611/5/3/008.

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11

Huang, Qing Qing, Guang Feng Chen, Jiang Hua Li, and Xin Wei. "Simulation on Trajectory Planning of 6R Manipulator Based on the Shortest Distance Criterion." Applied Mechanics and Materials 602-605 (August 2014): 942–45. http://dx.doi.org/10.4028/www.scientific.net/amm.602-605.942.

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This paper concerns the trajectory planning and simulation for 6R Manipulator. First, algebraic method was used to deduce the forward and inverse kinematics of 6R manipulator. All inverse solutions were expressed in atan2 to eliminate redundant roots to get the corresponding inverse formula. For the trajectory planning of manipulator in Cartesian space, using the cubic spline interpolation to get the drive function of joint, getting a unique solution from eight group inverses by the shortest distance criterion, and then obtained the actual end-effector trajectory. Using Matlab to verify the proposed trajectory planning method, validated results show that the proposed algorithm is feasible and effective.

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Verzhbitskiy, Mark Andreevich. "INVERSE PROBLEMS OF DETERMINING BOUNDARY REGIMES." Yugra State University Bulletin 13, no. 3 (September 15, 2017): 51–59. http://dx.doi.org/10.17816/byusu201713351-59.

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In the article we consider inverse problems for convective heat transfer models. We determine un- knowns occurring in the boundary conditions together with a solution to a parabolic second order system. The overdetermination conditions are integrals of a solution with weight. The existence and uniqueness theo- rems of solutions to this inverse problem is established.

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13

Tan, Yue Sheng, Peng Le Cheng, and Ai Ping Xiao. "Inverse Kinematics Solution for a 6R Special Configuration Manipulators Based on Screw Theory." Advanced Materials Research 216 (March 2011): 250–53. http://dx.doi.org/10.4028/www.scientific.net/amr.216.250.

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Three basic sub-problems of screw theory are acceptable for some particular configuration manipulators’ inverse kinematics, which can not solve the inverse kinematics of all configuration manipulators. This paper introduces two extra extended sub-problems, through which all inverse kinematic solutions for 6-R manipulators having closed-form inverse kinematics can be gained. The inverse kinematic solution for a new particular configuration manipulator is presented.

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14

Tseng, Wei-Kuo, Michael A. Earle, and Jiunn-Liang Guo. "Direct and Inverse Solutions with Geodetic Latitude in Terms of Longitude for Rhumb Line Sailing." Journal of Navigation 65, no. 3 (March 30, 2012): 549–59. http://dx.doi.org/10.1017/s0373463312000148.

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In this paper, equations are established to solve problems of Rhumb Line Sailing (RLS) on an oblate spheroid. Solutions are provided for both the inverse problem and the direct problem, thereby providing a complete solution to RLS. Development of these solutions was achieved in part by means of computer based symbolic algebra. The inverse solution described attains a high degree of accuracy for distance and azimuth. The direct solution has been obtained from a solution for latitude in terms of distance derived with the introduction of an inverse series expansion of meridian arc-length via the rectifying latitude. Also, a series to determine latitude at any longitude has been derived via the conformal latitude. This was achieved through application of Hermite's Interpolation Scheme or the Lagrange Inversion Theorem. Numerical examples show that the algorithms are very accurate and that the differences between original data and recovered data after applying the inverse or direct solution of RLS to recover the data calculated by the direct or inverse solution are very small. It reveals that the algorithms provided here are suitable for programming implementation and can be applied in the areas of maritime routing and cartographical computation in Graphical Information System (GIS) and Electronic Chart Display and Information System (ECDIS) environments.

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15

Kang, Chul-Goo. "Solution Space of Inverse Differential Kinematics." Journal of Korea Robotics Society 10, no. 4 (December 31, 2015): 230–44. http://dx.doi.org/10.7746/jkros.2015.10.4.230.

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16

Stroink, G. "Inverse problem solution in magnetisation studies." Physics in Medicine and Biology 32, no. 1 (January 1, 1987): 53–58. http://dx.doi.org/10.1088/0031-9155/32/1/008.

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17

Sapp, John L., Fady Dawoud, John C. Clements, and B. Milan Horáček. "Inverse Solution Mapping of Epicardial Potentials." Circulation: Arrhythmia and Electrophysiology 5, no. 5 (October 2012): 1001–9. http://dx.doi.org/10.1161/circep.111.970160.

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18

Galicki, Miroslaw. "Inverse Kinematics Solution to Mobile Manipulators." International Journal of Robotics Research 22, no. 12 (December 2003): 1041–64. http://dx.doi.org/10.1177/0278364903022012004.

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19

Göhmann, F., and V. E. Korepin. "Solution of the quantum inverse problem." Journal of Physics A: Mathematical and General 33, no. 6 (February 9, 2000): 1199–220. http://dx.doi.org/10.1088/0305-4470/33/6/308.

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20

Weber, Régine, and Jacques Hureau. "Numerical solution for various inverse problems." Journal of Computational and Applied Mathematics 115, no. 1-2 (March 2000): 577–91. http://dx.doi.org/10.1016/s0377-0427(99)00187-9.

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21

Shlenov, A. G. "Solution of inverse problems in magnetism." Measurement Techniques 35, no. 9 (September 1992): 1090–95. http://dx.doi.org/10.1007/bf00976849.

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22

Malik, M., and AJ Camm. "Solution to the Pacemaker Inverse Problem." Clinical Science 75, s19 (December 1, 1988): 7P—8P. http://dx.doi.org/10.1042/cs075007pc.

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23

Tolstikhin, Konstantin, and Berthold Scholtes. "An approach to solving an ill posed inverse problem of residual stress depth profiling in thin films and compact solid materials." Journal of Applied Crystallography 49, no. 4 (June 9, 2016): 1141–47. http://dx.doi.org/10.1107/s1600576716007676.

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The inverse problem of evaluating residual stresses σ(z) in real space using residual stresses σ(τ) in image space is discussed. This problem is ill posed and special solution methods are required in order to obtain a stable solution. Moreover, the real-space solution must be localized in reflecting layers only in multilayer systems. This requirement imposes strong restrictions on the solution methods and does not allow one to use methods based on the inverse Laplace transform employed for compact solid materials. Besides, in the case of solid materials, the use of the inverse Laplace transform often leads to extremely unstable solutions. The stable numerical solution of the discussed inverse problem can be found using a method based on the Tikhonov regularization. Given the measured data and their pointwise error estimation, this method provides stable approximate solutions for both solid materials and thin films in the form of piecewise functions defined solely in diffracting layers. The approximations are shown to converge to the exact function when the noise in the experimental data approaches zero. If the initial data satisfy certain constraints, the method provides a stable exact solution for the inverse problem. A freely available MATLAB package has been developed, and its efficiency was demonstrated in the numerical residual stress calculations carried out for solid materials and thin films.

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24

Wang, Peng, Yiren Zhou, and Nan Yan. "An Inverse Solution Algorithm for Industrial Robot." Journal of Physics: Conference Series 2173, no. 1 (January 1, 2022): 012085. http://dx.doi.org/10.1088/1742-6596/2173/1/012085.

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Abstract The inverse solution process of industrial robot is complex. Because the traditional matrix algorithm involves a lot of matrix operation, its process is complex. Numerical algorithms usually do not yield all the solutions, generally, the selection of initial value and the search algorithm have great influence on the convergence and accuracy. The geometric algorithms is simple and intuitionistic with simple expression and small computation. In this paper, a hybrid algorithm combining the geometric method and the inverse transformation matrix method is proposed for puma 560 industrial robots. The geometric algorithms is used to solve the first three joints and the matrix algorithm is used to obtain the final three joint angles. This paper introduces the inverse solution algorithm for this kind of robot in detail, and verifies the effectiveness of the proposed algorithm through matlab simulation.

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25

Dimovski, Igor, Mirjana Trompeska, Samoil Samak, Vladimir Dukovski, and Dijana Cvetkoska. "Algorithmic approach to geometric solution of generalized Paden–Kahan subproblem and its extension." International Journal of Advanced Robotic Systems 15, no. 1 (January 1, 2018): 172988141875515. http://dx.doi.org/10.1177/1729881418755157.

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Kinematics as a science of geometry of motion describes motion by means of position, orientation, and their time derivatives. The focus of this article aims screw theory approach for the solution of inverse kinematics problem. The kinematic elements are mathematically assembled through screw theory by using only the base, tool, and workpiece coordinate systems—opposite to conventional Denavit–Hartenberg approach, where at least n + 1 coordinate frames are needed for a robot manipulator with n joints. The inverse kinematics solution in Denavit–Hartenberg convention is implicit. Instead, explicit solutions to inverse kinematics using the Paden–Kahan subproblems could be expressed. This article gives step-by-step application of geometric algorithm for the solution of all the cases of Paden–Kahan subproblem 2 and some extension of that subproblem based on subproblem 2. The algorithm described here covers all of the cases that can appear in the generalized subproblem 2 definition, which makes it applicable for multiple movement configurations. The extended subproblem is used to solve inverse kinematics of a manipulator that cannot be solved using only three basic Paden–Kahan subproblems, as they are originally formulated. Instead, here is provided solution for the case of three subsequent rotations, where last two axes are parallel and the first one does not lie in the same plane with neither of the other axes. Since the inverse kinematics problem may have no solution, unique solution, or many solutions, this article gives a thorough discussion about the necessary conditions for the existence and number of solutions.

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26

Broderick, P. L., and R. J. Cipra. "A Method for Determining and Correcting Robot Position and Orientation Errors Due to Manufacturing." Journal of Mechanisms, Transmissions, and Automation in Design 110, no. 1 (March 1, 1988): 3–10. http://dx.doi.org/10.1115/1.3258902.

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A method is presented for calibration of a robot to correct position and orientation errors due to manufacturing. The method is based on the shape matrix robot kinematic description. Each joint is individually and successively moved in order to explicitly calculate the shape matrix of each link. In addition, methods to correct for the errors in both the forward and inverse kinematic solutions are presented. The modification of the forward solution is a simple task. The modification of the inverse kinematic solution is a difficult problem and is achieved by an iterative technique which supplements the closed-form solution. An example of the calibration and inverse solution is presented to show the improvement in the accuracy of the robot.

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27

SILVA, PEDRO V. "FINITE IDEMPOTENT INVERSE MONOID PRESENTATIONS." International Journal of Algebra and Computation 21, no. 07 (November 2011): 1111–33. http://dx.doi.org/10.1142/s0218196711006868.

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Several decidability problems for finite idempotent presentations of inverse monoids are solved, giving also insight into their structure. Besides providing a new elementary solution for the problem, solutions are obtained for the following problems: computing the maximal subgroups, being combinatorial, being semisimple, being fundamental, having infinite [Formula: see text]-classes. The word problem for the least fundamental quotient is also solved, with an unexpected consequence.

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Lyubanova, Anna Sh. "The Regularity of the Solutions of Inverse Problems for the Pseudoparabolic Equation." Journal of Siberian Federal University. Mathematics & Physics 14, no. 4 (July 2001): 414–24. http://dx.doi.org/10.17516/1997-1397-2021-14-4-414-424.

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The paper discusses the regularity of the solutions to the inverse problems on finding unknown coefficients dependent on t in the pseudoparabolic equation of the third order with an additional information on the boundary. By the regularity is meant the continuous dependence of the solution on the input data of the inverse problem. The regularity of the solution is proved for two inverse problems of recovering the unknown coefficient in the second order term and the leader term of the linear pseudoparabolic equation

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ABIAN, ALEXANDER, and PAULA A. KEMP. "THE NATURAL RIGHT AND THE NATURAL LEFT INVERSES OF RECTANGULAR MATRICES." Tamkang Journal of Mathematics 21, no. 3 (December 1, 1990): 279–86. http://dx.doi.org/10.5556/j.tkjm.21.1990.4690.

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If an $m$ by $n$ with $m < n$ matrix $A$ has a right inverse then it has infinitely many right inverses. In fact, $K (AK )^{-1}$ is a right inverse of $A$ for many $n$ by $m$ matrices $K$ of rank $m$. The natural choice for $K$ is the transpose $A'$ of $A$. Thus, we call $A'(AA')^{-1}$ the natural right inverse of $A$. It can be used (not so obviously) to solve $AX = C$ yielding the solution $X = A'(AA')^{-1}C$ which minimizes the length $||X||$. Similarly, if an $n$ by $m$ with $m < n$ matrix $B$ has a left inverse, we call $(B'B)^{-1}B'$ the natural left inverse of $B$. It can be used (in an obvious way) in an attempt "to solve" $BX =C$ yielding the best approximate solution $X =(B'B)^{-1}B'C$ which minimizes the error $|| BX||$.

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Mamytov, A. O. "ON A PROBLEM OF DETERMINING THE RIGHT-HAND SIDE OF THE PARTIAL INTEGRO-DIFFERENTIAL EQUATION." Bulletin of the South Ural State University series "Mathematics. Mechanics. Physics" 13, no. 3 (2021): 31–38. http://dx.doi.org/10.14529/mmph210304.

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As it is known, in the inverse problem, apart from the sought-for “basic” solution of the problem (i. e., the solution of the direct problem), the components of the direct problem are unknown. It is required to find these unknown components, so they will be also included in the solution of the inverse problem. To determine these components in the inverse problem, some additional information on the solution of the direct problem is added to the given equations. The additional information is called the inverse problem data. In the proposed article, the specific fourth-order partial integro-differential equation with the known initial and boundary conditions is considered. For simplicity, the homogeneous boundary conditions have been examined, since with the help of a linear transformation, the always inhomogeneous boundary conditions can be reduced to the homogeneous ones. The right-hand side of the equation contains n unknown functions: φi(t), i = 1,2,…,n.. To determine these unknown functions: φi(t), i = 1,2,…,n in the inverse problem there is additional information on the solution of the direct problem, i.e., the values of the sought-for “basic” solution to the problem in the inner segments of the investigated region are known, i. e., u(t,xi) = gi(t), t∈[0,T], xi∈ (0,1), i = 1,2,…,n. The problem is investigated in a rectangle located in the first quarter of the Cartesian coordinate system. To solve the inverse problem, an algorithm has been elaborated and sufficient conditions for the existence and the uniqueness of the solution of the inverse problem for the restoration of the right-hand side in a fourth-order partial integrodifferential equation have been found. When solving the inverse problem, the methods of transformations, Green's function, solutions of systems of linear Volterra integral equations have been used. As a result, the inverse problem has been reduced to a system of (n + 1) linear Volterra integral equations of the second kind, the solution of which for small 0 < T exists and is unique. The considered inverse problem can be called the inverse source problem.

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31

Ravshanov, Normaxmad, and Bozorboy Yusupovich Palvanov. "NUMERICAL SOLUTION OF INVERSE PROBLEMS FILTERING PROCESS OF LOW-CONCENTRATION SOLUTIONS." Theoretical & Applied Science 48, no. 04 (April 30, 2017): 137–44. http://dx.doi.org/10.15863/tas.2017.04.48.22.

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32

Friedman, Diana C. W., Tim Kowalewski, Radivoje Jovanovic, Jacob Rosen, and Blake Hannaford. "Freeing the Serial Mechanism Designer from Inverse Kinematic Solvability Constraints." Applied Bionics and Biomechanics 7, no. 3 (2010): 209–16. http://dx.doi.org/10.1155/2010/605978.

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This paper presents a fast numerical solution for the inverse kinematics of a serial manipulator. The method is implemented on the C-arm, a manipulator designed for use in robotic surgery. The inverse kinematics solution provides all possible solutions for any six degree-of-freedom serial manipulator, assuming that the forward kinematics are known and that it is possible to solve for the remaining joint angles if one joint angle’s value is known. With a fast numerical method and the current levels of computing power, designing a manipulator with closed-form inverse kinematics is no longer necessary. When designing the C-arm, we therefore chose to weigh other factors, such as actuator size and patient safety, more heavily than the ability to find a closed-form inverse kinematics solution.

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Bannikova, T. M., V. M. Nemtsov, N. A. Baranova, G. N. Konygin, and O. M. Nemtsova. "A method for estimating the statistical error of the solution in the inverse spectroscopy problem." Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta 58 (November 2021): 3–17. http://dx.doi.org/10.35634/2226-3594-2021-58-01.

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A method for obtaining the interval of statistical error of the solution of the inverse spectroscopy problem, for the estimation of the statistical error of experimental data of which the normal distribution law can be applied, has been proposed. With the help of mathematical modeling of the statistical error of partial spectral components obtained from the numerically stable solution of the inverse problem, it has become possible to specify the error of the corresponding solution. The problem of getting the inverse solution error interval is actual because the existing methods of solution error evaluation are based on the analysis of smooth functional dependences under rigid restrictions on the region of acceptable solutions (compactness, monotonicity, etc.). Their use in computer processing of real experimental data is extremely difficult and therefore, as a rule, is not applied. Based on the extraction of partial spectral components and the estimation of their error, a method for obtaining an interval of statistical error for the solution of inverse spectroscopy problems has been proposed in this work. The necessity and importance of finding the solution error interval to provide reliable results is demonstrated using examples of processing Mössbauer spectra.

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Al Horani, Mohammed, Mauro Fabrizio, Angelo Favini, and Hiroki Tanabe. "Inverse Problems for Degenerate Fractional Integro-Differential Equations." Mathematics 8, no. 4 (April 3, 2020): 532. http://dx.doi.org/10.3390/math8040532.

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This paper deals with inverse problems related to degenerate fractional integro-differential equations in Banach spaces. We study existence, uniqueness and regularity of solutions to the problem, claiming to extend well known studies for the case of non-fractional equations. Our method is based on transforming the inverse problem to a direct problem and identifying the conditions under which this direct problem has a unique solution. The conditions under which the unique strict solution can be compared with the case of a mild solution, obtained in previous studies under quite restrictive requirements, are on the underlying functions. Applications from partial differential equations are given to illustrate our abstract results.

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Kamyab, Shima, Zohreh Azimifar, Rasool Sabzi, and Paul Fieguth. "Deep learning methods for inverse problems." PeerJ Computer Science 8 (May 2, 2022): e951. http://dx.doi.org/10.7717/peerj-cs.951.

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In this paper we investigate a variety of deep learning strategies for solving inverse problems. We classify existing deep learning solutions for inverse problems into three categories of Direct Mapping, Data Consistency Optimizer, and Deep Regularizer. We choose a sample of each inverse problem type, so as to compare the robustness of the three categories, and report a statistical analysis of their differences. We perform extensive experiments on the classic problem of linear regression and three well-known inverse problems in computer vision, namely image denoising, 3D human face inverse rendering, and object tracking, in presence of noise and outliers, are selected as representative prototypes for each class of inverse problems. The overall results and the statistical analyses show that the solution categories have a robustness behaviour dependent on the type of inverse problem domain, and specifically dependent on whether or not the problem includes measurement outliers. Based on our experimental results, we conclude by proposing the most robust solution category for each inverse problem class.

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Miladinovic, Marko, Sladjana Miljkovic, and Predrag Stanimirovic. "Minimal properties of the Drazin-inverse solution of a matrix equation." Filomat 28, no. 2 (2014): 383–95. http://dx.doi.org/10.2298/fil1402383m.

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We present the Drazin-inverse solution of the matrix equation AXB = G as a least-squares solution of a specified minimization problem. Some important properties of the Moore-Penrose inverse are extended on the Drazin inverse by exploring the minimal norm properties of the Drazin-inverse solution of the matrix equation AXB = G. The least squares properties of the Drazin-inverse solution lead to new representations of the Drazin inverse of a given matrix, which are justified by illustrative examples.

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PARK, HYUNGJU ANDY, MUHAMMAD AHMAD ALI, and C. S. GEORGE LEE. "CLOSED-FORM INVERSE KINEMATIC POSITION SOLUTION FOR HUMANOID ROBOTS." International Journal of Humanoid Robotics 09, no. 03 (September 2012): 1250022. http://dx.doi.org/10.1142/s0219843612500223.

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This paper focuses on developing a consistent methodology for deriving a closed-form inverse kinematic joint solution of a humanoid robot with decision equations to select a proper solution from multiple solutions. Most researchers resort to iterative methods for inverse kinematics using the Jacobian matrix to avoid the difficulty of finding a closed-form joint solution. Since a closed-form joint solution, if available, has many advantages over iterative methods, we have developed a novel reverse-decoupling method by viewing the kinematic chain of a limb of a humanoid robot in reverse order and then decoupling it into the positioning and orientation mechanisms, and finally utilizing the inverse-transform technique to derive a consistent joint solution for the humanoid robot. The proposed method presents a simple and efficient procedure for finding the joint solution for most of the existing humanoid robots. Extensive computer simulations of the proposed approach on a Hubo KHR-4 humanoid robot show that it can be applied easily to most humanoid robots such as HOAP-2, HRP-2 and ASIMO humanoid robots with slight modifications.

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Pohl, E. D., and H. Lipkin. "Complex Robotic Inverse Kinematic Solutions." Journal of Mechanical Design 115, no. 3 (September 1, 1993): 509–14. http://dx.doi.org/10.1115/1.2919219.

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A new method exploiting complex numbers in the inverse kinematic solution of serial robotic manipulators is presented. If a prescribed end effector location is outside of the manipulator workspace, complex joint values result. While they cannot be implemented physically, they may be mapped to real numbers. The result approximates the prescribed location. For many industrial manipulators, mapped solutions may be explained using spherical and planar dyads. An important criterion characterizes error minimization properties, and is illustrated for a 3R regional robot.

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39

Choulli, M. "An abstract inverse problem." Journal of Applied Mathematics and Stochastic Analysis 4, no. 2 (January 1, 1991): 117–28. http://dx.doi.org/10.1155/s1048953391000084.

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In this paper we consider an inverse problem that corresponds to an abstract integrodifferential equation. First, we prove a local existence and uniqueness theorem. We also show that every continuous solution can be locally extended in a unique way. Finally, we give sufficient conditions for the existence and a stability of the global solution.

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40

Aytzhanov, S. E., and G. R. Ashurova. "THE SOLVABILITY OF THE INVERSE PROBLEM FOR THE SOBOLEV TYPE EQUATION." BULLETIN Series of Physics & Mathematical Sciences 70, no. 2 (June 30, 2020): 26–35. http://dx.doi.org/10.51889/2020-2.1728-7901.04.

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The study of nonlinear equations of mathematical physics, including inverse problems, is currently relevant. This work is devoted to the fundamental problem of investigating the qualitative properties of the inverse problem for pseudoparabolic equations (also called Sobolev-type equations) with a sufficiently smooth boundary. In the article, the Galerkin method proves the existence of a weak solution to the inverse problem in a bounded domain. Using Sobolev embedding theorems, a priori estimates of the solution are obtained. Using Galerkin approximations, you can get a top-down estimate of the existence of the solution. A local and global theorem on the existence of a solution are obtained. We consider the problems of asymptotic behavior of solutions at, as well as blow-up in finite time. Sufficient conditions for t→∞ the "blow-up" of the solution in a finite time are obtained, and a lower estimate of the blow-up of the solution is obtained.

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Li, Fan-Liang. "Left and right inverse eigenpairs problem with a submatrix constraint for the generalized centrosymmetric matrix." Open Mathematics 18, no. 1 (June 18, 2020): 603–15. http://dx.doi.org/10.1515/math-2020-0020.

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Abstract Left and right inverse eigenpairs problem is a special inverse eigenvalue problem. There are many meaningful results about this problem. However, few authors have considered the left and right inverse eigenpairs problem with a submatrix constraint. In this article, we will consider the left and right inverse eigenpairs problem with the leading principal submatrix constraint for the generalized centrosymmetric matrix and its optimal approximation problem. Combining the special properties of left and right eigenpairs and the generalized singular value decomposition, we derive the solvability conditions of the problem and its general solutions. With the invariance of the Frobenius norm under orthogonal transformations, we obtain the unique solution of optimal approximation problem. We present an algorithm and numerical experiment to give the optimal approximation solution. Our results extend and unify many results for left and right inverse eigenpairs problem and the inverse eigenvalue problem of centrosymmetric matrices with a submatrix constraint.

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42

Andrew, Alan L. "Numerical solution of inverse Sturm--Liouville problems." ANZIAM Journal 45 (June 1, 2004): 326. http://dx.doi.org/10.21914/anziamj.v45i0.891.

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Açil, M., and N. Bildik. "A SOLUTION TO INVERSE STURM-LIOUVILLE PROBLEMS." Advances in Mathematics: Scientific Journal 10, no. 9 (September 8, 2021): 3165–74. http://dx.doi.org/10.37418/amsj.10.9.6.

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In this study, we recover potential function and separable boundary conditions for the inverse Sturm-Liouville problem in normal form by using two partial subsets of the data which consist of its one spectrum and sequence of endpoints of eigenfunctions.

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Khromov, A. A. "The Solution of a Certain Inverse Problem." Izvestiya of Saratov University. New Series. Series: Mathematics. Mechanics. Informatics 16, no. 2 (June 14, 2016): 180–83. http://dx.doi.org/10.18500/1816-9791-2016-16-2-180-183.

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Venkataraman, P. "Solution of inverse ODE using Bezier functions." Inverse Problems in Science and Engineering 19, no. 4 (June 2011): 529–49. http://dx.doi.org/10.1080/17415977.2010.531465.

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Ahmad, Ghandi F., Dana H. Brooks, and Robert S. MacLeod. "An Admissible Solution Approach to Inverse Electrocardiography." Annals of Biomedical Engineering 26, no. 2 (March 1998): 278–92. http://dx.doi.org/10.1114/1.56.

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Vabishchevich, P. N., V. I. Vasil’ev, M. V. Vasil’eva, and D. Ya Nikiforov. "Numerical solution of an inverse filtration problem." Lobachevskii Journal of Mathematics 37, no. 6 (November 2016): 777–86. http://dx.doi.org/10.1134/s1995080216060056.

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Nan-xian, Chen, and Rong Er-qian. "Unified solution of the inverse capacity problem." Physical Review E 57, no. 2 (February 1, 1998): 1302–8. http://dx.doi.org/10.1103/physreve.57.1302.

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Zu, Di. "EFFICIENT INVERSE KINEMATIC SOLUTION FOR REDUNDANT MANIPULATORS." Chinese Journal of Mechanical Engineering 41, no. 06 (2005): 71. http://dx.doi.org/10.3901/jme.2005.06.071.

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Nievergelt, Yves. "Solution to an Inverse Problem in Diffusion." SIAM Review 40, no. 1 (January 1998): 74–80. http://dx.doi.org/10.1137/s003614459630757x.

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Journal articles on the topic 'Inverse solution'

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