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...transform for 3D symmetric tensor fields with sources on a curve." Inverse problems 22.2 (2006): 399.</ref> ...Longitudinal Ray Transform for 2D residual elastic strain fields." Inverse Problems 40.7 (2024): 075011.</ref> and Doppler tomography of velocity vector fields ...

...|regularization]] method for obtaining meaningful solutions to ill-posed [[inverse problem]]s. Where other regularization methods, such as the frequently use Given a data array '''X''', the basic Backus-Gilbert inverse is: ...

* V. A. Kozlov, V.G. Maz'ya, J. Rossmann, "Elliptic boundary value problems in domains with point singularities", Amer. Math. Soc. (1997) [https://www. * A. T. Prilepko, D.G. Orlovsky, I.A. Vasin, "Methods for solving inverse problems in mathematical physics", M. Dekker (2000) [https://www.ams.org/mathscinet- ...

...They are particularly useful in the study of [[Bayesian inference|inverse problems]] on [[function space]]s for which a Gaussian [[prior probability|Bayesian |s2cid=88518742 | title = Besov priors for Bayesian inverse problems ...

...thematics)|regularized]] [[matrix (mathematics)|matrix]] [[inverse problem|inverse method]] based on [[Bayes' theorem]]. A matrix inverse problem looks like this: ...

...linear [[inverse problems]], and it has been extended to solve non-linear problems that involve constraints. The method was first proposed in the 1950s by [[L For [[ill-posed]] problems, the iterative method needs to be stopped at a suitable iteration index, be ...

...<math>\operatorname{Cay}(G,S)\cong \operatorname{Cay}(G,T)</math> for some inverse closed subsets <math>S</math> and <math>T</math> of <math>G\setminus \{1\}< * [[List of unsolved problems in mathematics]] ...

...(or a matrix) that possibly has a bad [[condition number]] or an unbounded inverse. In this context, regularization amounts to substituting the original opera ...h> given <math>g</math>. If the solution exists, is unique and stable, the inverse problem (i.e. the problem of solving for <math>f</math>) is well-posed; oth ...

...thematics. One major area of study in additive combinatorics are ''inverse problems'': given the size of the [[sumset]] {{Math|''A'' + ''B''}} is small, what c ...owever, in literature, such problems are sometimes considered to be direct problems as well. Examples of this type include the [[Erdős–Heilbronn conjecture|Erd ...

...on the solution of infinite domain, thin-walled structures, and [[inverse problems]]. ...n found very competitive to some application areas such as infinite domain problems. ...

...ion from the known ones. It is widely used in [[Inverse scattering problem|inverse scattering theory]], in the theory of [[orthogonal polynomials]],<ref>{{cit ...rboux transformations and the factorization of generalized Sturm–Liouville problems | journal=Proceedings of the Royal Society of Edinburgh: Section a Mathemat ...

* [http://www.resistivity.net Solution of inverse problem] [[Category:Inverse problems]] ...

...orm of projection used to solve non-differentiable [[convex optimization]] problems. Many interesting problems can be formulated as convex optimization problems of the form ...

...|Stoll|1995}}</ref> It appears in [[Galois theory]], in the study of the [[inverse Galois problem]] or the [[embedding problem]] which is a generalization of *Finite semiabelian groups possess [[Inverse Galois problem|G-realizations]]<ref>{{harv|Malle|Matzat|1999|p=33}}</ref><r ...

...nomenon has been used to prove corresponding near-linear bounds on various problems in [[discrete geometry]], for instance showing that the unbounded face of a ...e superlinearity is described in terms of the [[Ackermann function#Inverse|inverse Ackermann function]] <math>\alpha(n)</math>. For instance, the length of a ...

and its inverse transform: And the inverse transform is given by the MATLAB code: ...

...od]] is not trivial especially for moving boundary, and higher-dimensional problems. The boundary knot method is different from the other methods based on the ...s with relatively a small number of nodes for various linear and nonlinear problems. ...

The inverse of above is the {{math|'''H'''}}-transform of the same order; for a given f ...the Hankel, {{math|''Y''}}, {{math|'''H'''}} transforms all may appear in problems having [[axial symmetry]]. ...

...19–236 | year=1997 | doi=10.1002/mana.19971880113 }}</ref> Conversely, the inverse fLT (ifLT) reconstructs the original function from the components of the Le ...sy experimental outcome ''s''(''t'') and the subsequent application of the inverse fLT (ifLT) on an appropriately truncated Legendre spectrum of ''s''(''t'') ...

...hor=S.N. Bernstein | authorlink=Sergei Natanovich Bernstein | title=On the inverse problem of the theory of the best approximation of continuous functions | j ...nd Its Applications | number=49 | title=Fixed-Point Algorithms for Inverse Problems in Science and Engineering | year=2011 | volume=49 | isbn=9781441995681 | d ...