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Journal articles on the topic 'Lagrange inversion'

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Published: 4 June 2021
Last updated: 10 February 2022

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1

Gessel, Ira M. "Lagrange inversion." Journal of Combinatorial Theory, Series A 144 (November 2016): 212–49. http://dx.doi.org/10.1016/j.jcta.2016.06.018.

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2

Abd El-Salam, F. A. "-Dimensional Fractional Lagrange's Inversion Theorem." Abstract and Applied Analysis 2013 (2013): 1–11. http://dx.doi.org/10.1155/2013/310679.

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Using Riemann-Liouville fractional differential operator, a fractional extension of the Lagrange inversion theorem and related formulas are developed. The required basic definitions, lemmas, and theorems in the fractional calculus are presented. A fractional form of Lagrange's expansion for one implicitly defined independent variable is obtained. Then, a fractional version of Lagrange's expansion in more than one unknown function is generalized. For extending the treatment in higher dimensions, some relevant vectors and tensors definitions and notations are presented. A fractional Taylor expansion of a function of -dimensional polyadics is derived. A fractional -dimensional Lagrange inversion theorem is proved.
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3

Gessel, Ira M., and Gilbert Labelle. "Lagrange inversion for species." Journal of Combinatorial Theory, Series A 72, no. 1 (October 1995): 95–117. http://dx.doi.org/10.1016/0097-3165(95)90030-6.

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4

Greene, John. "Lagrange inversion over finite fields." Pacific Journal of Mathematics 130, no. 2 (December 1, 1987): 313–25. http://dx.doi.org/10.2140/pjm.1987.130.313.

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5

Singer, D. "Q-Analogues of Lagrange Inversion." Advances in Mathematics 115, no. 1 (September 1995): 99–116. http://dx.doi.org/10.1006/aima.1995.1051.

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6

Grossman, Nathaniel. "A C∞ Lagrange Inversion Theorem." American Mathematical Monthly 112, no. 6 (June 2005): 512–14. http://dx.doi.org/10.1080/00029890.2005.11920222.

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7

Dongsheng, Yin, and Shen Fuxing. "An application of Lagrange inversion." Tamkang Journal of Mathematics 32, no. 1 (March 31, 2001): 9–13. http://dx.doi.org/10.5556/j.tkjm.32.2001.361.

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8

Merlini, D., R. Sprugnoli, and M. C. Verri. "Lagrange Inversion: When and How." Acta Applicandae Mathematicae 94, no. 3 (December 12, 2006): 233–49. http://dx.doi.org/10.1007/s10440-006-9077-7.

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9

Grossman, Nathaniel. "A $C^\infty$ Lagrange Inversion Theorem." American Mathematical Monthly 112, no. 6 (June 1, 2005): 512. http://dx.doi.org/10.2307/30037521.

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10

Barnabei, Marilena. "Lagrange inversion in infinitely many variables." Journal of Mathematical Analysis and Applications 108, no. 1 (May 1985): 198–210. http://dx.doi.org/10.1016/0022-247x(85)90016-2.

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11

Novelli, Jean-Christophe, and Jean-Yves Thibon. "Noncommutative symmetric functions and Lagrange inversion." Advances in Applied Mathematics 40, no. 1 (January 2008): 8–35. http://dx.doi.org/10.1016/j.aam.2007.05.005.

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12

Kuznetsov, Alexey. "Lagrange Inversion Theorem for Dirichlet series." Journal of Mathematical Analysis and Applications 493, no. 2 (January 2021): 124575. http://dx.doi.org/10.1016/j.jmaa.2020.124575.

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13

Huang, Jianfeng, and Xinrong Ma. "A Determinant Identity Implying the Lagrange–Good Inversion Formula." Proceedings of the Edinburgh Mathematical Society 60, no. 1 (June 13, 2016): 165–76. http://dx.doi.org/10.1017/s0013091516000031.

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AbstractIn this paper a determinant identity is established, from which a simple proof of the multivariate Lagrange–Good inversion formula follows directly. Further discussion on a discrete analogue of the Lagrange–Good inversion formula is also presented.
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14

Krattenthaler, Ch. "Operator methods and Lagrange inversion: a unified approach to Lagrange formulas." Transactions of the American Mathematical Society 305, no. 2 (February 1, 1988): 431. http://dx.doi.org/10.1090/s0002-9947-1988-0924765-4.

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15

HUANG, I.-CHIAU. "TWO APPROACHES TO MÖBIUS INVERSION." Bulletin of the Australian Mathematical Society 85, no. 1 (August 15, 2011): 68–78. http://dx.doi.org/10.1017/s0004972711002656.

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16

Qi, Ming Long, Luo Zhong, and Qing Ping Guo. "On Inversion Algorithms over Optimal Extension Fields Using Lagrange Representation." Applied Mechanics and Materials 20-23 (January 2010): 277–82. http://dx.doi.org/10.4028/www.scientific.net/amm.20-23.277.

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We present, illustrate and analyze some basic notions of the Lagrange Representation (LR) over finite fields, and elementary theory of Optimal Extension Fields. In combining the Lagrange Representation theory and the Frobenius mapping theorem, we could establish an inversion algorithm in the LR version. Our contribution is of adapting an addition-chain-like method over an Optimal Extension Field to the Lagrange Representation.
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17

Gessel, Ira, and Dennis Stanton. "Another family of q-Lagrange inversion formulas." Rocky Mountain Journal of Mathematics 16, no. 2 (June 1986): 373–84. http://dx.doi.org/10.1216/rmj-1986-16-2-373.

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18

Peiffer, K. "On inversion of the lagrange-dirichlet theorem." Journal of Applied Mathematics and Mechanics 55, no. 4 (January 1991): 436–41. http://dx.doi.org/10.1016/0021-8928(91)90002-c.

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19

Verde-Star, Luis. "Dual operators and Lagrange inversion in several variables." Advances in Mathematics 58, no. 1 (October 1985): 89–108. http://dx.doi.org/10.1016/0001-8708(85)90050-7.

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20

Krantz, Steven G., and Harold R. Parks. "The Lagrange inversion theorem in the smooth case." Journal of Mathematical Analysis and Applications 340, no. 2 (April 2008): 1263–70. http://dx.doi.org/10.1016/j.jmaa.2007.09.039.

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21

Zeng, Jiang. "The β-Extension of the Multivariable Lagrange Inversion Formula." Studies in Applied Mathematics 84, no. 2 (February 1991): 167–82. http://dx.doi.org/10.1002/sapm1991842167.

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22

Niederhausen, Heinrich. "Fast Lagrange inversion, with an application to factorial numbers." Discrete Mathematics 104, no. 1 (June 1992): 99–110. http://dx.doi.org/10.1016/0012-365x(92)90628-s.

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23

Gessel, Ira M. "A combinatorial proof of the multivariable lagrange inversion formula." Journal of Combinatorial Theory, Series A 45, no. 2 (July 1987): 178–95. http://dx.doi.org/10.1016/0097-3165(87)90013-6.

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24

Jansen, Sabine, Tobias Kuna, and Dimitrios Tsagkarogiannis. "Lagrange Inversion and Combinatorial Species with Uncountable Color Palette." Annales Henri Poincaré 22, no. 5 (February 11, 2021): 1499–534. http://dx.doi.org/10.1007/s00023-020-01013-0.

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AbstractWe prove a multivariate Lagrange-Good formula for functionals of uncountably many variables and investigate its relation with inversion formulas using trees. We clarify the cancellations that take place between the two aforementioned formulas and draw connections with similar approaches in a range of applications.
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25

BULTEL, JEAN-PAUL. "A ONE-PARAMETER DEFORMATION OF THE NONCOMMUTATIVE LAGRANGE INVERSION FORMULA." International Journal of Algebra and Computation 21, no. 08 (December 2011): 1395–414. http://dx.doi.org/10.1142/s0218196711006662.

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We give a one-parameter deformation of the noncommutative Lagrange inversion formula, more precisely, of the formula of Brouder–Frabetti–Krattenthaler for the antipode of the noncommutative Faá di Bruno algebra. Namely, we obtain a closed formula for the antipode of the one-parameter deformation of this Hopf algebra discovered by Foissy.
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26

Brassesco, Stella, and Miguel A. Méndez. "The asymptotic expansion for n! and the Lagrange inversion formula." Ramanujan Journal 24, no. 2 (June 12, 2010): 219–34. http://dx.doi.org/10.1007/s11139-010-9237-2.

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27

Kozlov, V. V. "Asymptotic motions and the inversion of the lagrange-dirichlet theorem." Journal of Applied Mathematics and Mechanics 50, no. 6 (January 1986): 719–25. http://dx.doi.org/10.1016/0021-8928(86)90079-1.

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28

Yin, Juan, and Sheng-Liang Yang. "On the r-Central Coefficient Matrices of the Catalan Triangles." Journal of Discrete Mathematics 2015 (January 5, 2015): 1–4. http://dx.doi.org/10.1155/2015/209045.

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We introduce the definition of the r-central coefficient matrices of a given Riordan array. Applying this definition and Lagrange Inversion Formula, we can calculate the r-central coefficient matrices of Catalan triangles and obtain some interesting triangles and sequences.
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29

Demni, Nizar. "Lagrange inversion formula, Laguerre polynomials and the free unitary Brownian motion." Journal of Operator Theory 78, no. 1 (July 2017): 179–200. http://dx.doi.org/10.7900/jot.2016jun19.2139.

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30

Böhm, W. "Multivariate Lagrange inversion and the maximum of a persistent random walk." Journal of Statistical Planning and Inference 101, no. 1-2 (February 2002): 23–31. http://dx.doi.org/10.1016/s0378-3758(01)00149-5.

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31

Vu, Viet T., Thomas K. Sjogren, and Mats I. Pettersson. "Two-Dimensional Spectrum for BiSAR Derivation Based on Lagrange Inversion Theorem." IEEE Geoscience and Remote Sensing Letters 11, no. 7 (July 1, 2014): 1210–14. http://dx.doi.org/10.1109/lgrs.2013.2289735.

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32

Abdesselam, Abdelmalek. "A physicist s proof of the Lagrange–Good multivariable inversion formula." Journal of Physics A: Mathematical and General 36, no. 36 (August 27, 2003): 9471–77. http://dx.doi.org/10.1088/0305-4470/36/36/304.

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33

Gay, Roger, Marcel Grangé, and Ahmed Sebbar. "Sur Deux Formules De Frobenius et Stickelberger et Inversion De Lagrange." Complex Analysis and Operator Theory 10, no. 1 (October 23, 2015): 29–60. http://dx.doi.org/10.1007/s11785-015-0504-5.

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34

Haiman, Mark, and William Schmitt. "Incidence algebra antipodes and lagrange inversion in one and several variables." Journal of Combinatorial Theory, Series A 50, no. 2 (March 1989): 172–85. http://dx.doi.org/10.1016/0097-3165(89)90013-7.

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35

Goulden, I. P., and D. M. Kulkarni. "Multivariable Lagrange Inversion, Gessel-Viennot Cancellation, and the Matrix Tree Theorem." Journal of Combinatorial Theory, Series A 80, no. 2 (November 1997): 295–308. http://dx.doi.org/10.1006/jcta.1997.2827.

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36

Xia, Yuxuan, and Zhenyu Cui. "An exact and explicit implied volatility inversion formula." International Journal of Financial Engineering 05, no. 03 (September 2018): 1850032. http://dx.doi.org/10.1142/s2424786318500329.

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In this paper, we develop an exact and explicit (model-independent) Taylor series representation of the implied volatility based on the novel applications of an extended Faà di Bruno formula under the operator calculus setting, and the Lagrange inversion theorem. We rigorously establish that our formula converges to the true implied volatility as the truncation order increases. Numerical examples illustrate the remarkable accuracy and efficiency of the formula. The formula distinguishes from previous literature as it converges to the true exact implied volatility, is a closed-form formula whose coefficients are explicitly determined and do not involve numerical iterations.
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37

Palamodov, V. P. "On inversion of the Lagrange–Dirichlet theorem and instability of conservative systems." Russian Mathematical Surveys 75, no. 3 (June 2020): 495–508. http://dx.doi.org/10.1070/rm9945.

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38

Hsu, Leetsch C. "Some theorems on Stirling-type pairs." Proceedings of the Edinburgh Mathematical Society 36, no. 3 (October 1993): 525–35. http://dx.doi.org/10.1017/s0013091500018599.

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It is shown that an extended Schlömilch formula for Stirling-type pairs of numbers and the inversion formula of Lagrange are implied by each other. Also proved are some congruence relations modulo a prime number p(>2) associated with generalized Stirling numbers. The third result is concerned with the asymptotic expansions of Stirling-type pairs involving large parameters.
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39

Josuat-Vergès, Matthieu. "Δ-Cumulants in terms of moments." Infinite Dimensional Analysis, Quantum Probability and Related Topics 21, no. 02 (June 2018): 1850012. http://dx.doi.org/10.1142/s0219025718500121.

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The [Formula: see text]-convolution of real probability measures, introduced by Bożejko, generalizes both free and Boolean convolutions. It is linearized by the [Formula: see text]-cumulants, and Yoshida gave a combinatorial formula for moments in terms of [Formula: see text]-cumulants, that implicitly defines the latter. It relies on the definition of an appropriate weight on noncrossing partitions. We give here two different expressions for the [Formula: see text]-cumulants: the first one is a simple variant of Lagrange inversion formula, and the second one is a combinatorial inversion of Yoshida’s formula involving Schröder trees.
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40

Nevison, Cynthia, Arlyn Andrews, Kirk Thoning, Ed Dlugokencky, Colm Sweeney, Scot Miller, Eri Saikawa, et al. "Nitrous Oxide Emissions Estimated With the CarbonTracker‐Lagrange North American Regional Inversion Framework." Global Biogeochemical Cycles 32, no. 3 (March 2018): 463–85. http://dx.doi.org/10.1002/2017gb005759.

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41

Viskov, O. V. "A Random Walk with a Skip-Free Component and the Lagrange Inversion Formula." Theory of Probability & Its Applications 45, no. 1 (January 2001): 164–72. http://dx.doi.org/10.1137/s0040585x97978105.

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42

CORREA-RESTREPO, DARÍO, and DIETER PFIRSCH. "Poisson brackets for guiding-centre and gyrocentre theories." Journal of Plasma Physics 71, no. 1 (January 13, 2005): 1–10. http://dx.doi.org/10.1017/s0022377804002910.

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Poisson brackets in the phase space of averaging Kruskal coordinates are obtained in a clear and straightforward way. The derivation makes use of the equations of motion of guiding centres and gyrocentres derived from a gyroangle-independent Lagrangian, and from generally valid relations of Hamiltonian mechanics. The usual procedure of matrix inversion to obtain the Poisson tensor from the Lagrange tensor is not required.
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43

Zhang, Xuebo, Haining Huang, Wenwei Ying, Huakui Wang, and Jun Xiao. "An Indirect Range-Doppler Algorithm for Multireceiver Synthetic Aperture Sonar Based on Lagrange Inversion Theorem." IEEE Transactions on Geoscience and Remote Sensing 55, no. 6 (June 2017): 3572–87. http://dx.doi.org/10.1109/tgrs.2017.2676339.

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44

Chen, Xing, Tianzhu Yi, Feng He, Zhihua He, and Zhen Dong. "An Improved Generalized Chirp Scaling Algorithm Based on Lagrange Inversion Theorem for High-Resolution Low Frequency Synthetic Aperture Radar Imaging." Remote Sensing 11, no. 16 (August 10, 2019): 1874. http://dx.doi.org/10.3390/rs11161874.

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The high-resolution low frequency synthetic aperture radar (SAR) has serious range-azimuth phase coupling due to the large bandwidth and long integration time. High-resolution SAR processing methods are necessary for focusing the raw data of such radar. The generalized chirp scaling algorithm (GCSA) is generally accepted as an attractive solution to focus SAR systems with low frequency, large bandwidth and wide beam bandwidth. However, as the bandwidth and/or beamwidth increase, the serious phase coupling limits the performance of the current GCSA and degrades the imaging quality. The degradation is mainly caused by two reasons: the residual high-order coupling phase and the non-negligible error introduced by the linear approximation of stationary phase point using the principle of stationary phase (POSP). According to the characteristics of a high-resolution low frequency SAR signal, this paper firstly presents a principle to determine the required order of range frequency. After compensating for the range-independent coupling phase above 3rd order, an improved GCSA based on Lagrange inversion theorem is analytically derived. The Lagrange inversion enables the high-order range-dependent coupling phase to be accurately compensated. Imaging results of P- and L-band SAR data demonstrate the excellent performance of the proposed algorithm compared to the existing GCSA. The image quality and focusing depth in range dimension are greatly improved. The improved method provides the possibility to efficiently process high-resolution low frequency SAR data with wide swath.
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45

Codd, A. L., and L. Gross. "Three-dimensional inversion for sparse potential data using first-order system least squares with application to gravity anomalies in Western Queensland." Geophysical Journal International 227, no. 3 (August 13, 2021): 2095–120. http://dx.doi.org/10.1093/gji/ggab323.

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SUMMARY We present an inversion algorithm tailored for point gravity data. As the data are from multiple surveys, it is inconsistent with regards to spacing and accuracy. An algorithm design objective is the exact placement of gravity observations to ensure no interpolation of the data is needed prior to any inversion. This is accommodated by discretization using an unstructured tetrahedral finite-element mesh for both gravity and density with mesh nodes located at all observation points and a first-order system least-squares (FOSLS) formulation for the gravity modelling equations. Regularization follows the Bayesian framework where we use a differential operator approximation of an exponential covariance kernel, avoiding the usual requirement of inverting large dense covariance matrices. Rather than using higher order basis functions with continuous derivatives across element faces, regularization is also implemented with a FOSLS formulation using vector-valued property function (density and its gradient). Minimization of the cost function, comprised of data misfit and regularization, is achieved via a Lagrange multiplier method with the minimum of the gravity FOSLS functional as a constraint. The Lagrange variations are combined into a single equation for the property function and solved using an integral form of the pre-conditioned conjugate gradient method (I-PCG). The diagonal entries of the regularization operator are used as the pre-conditioner to minimize computational costs and memory requirements. Discretization of the differential operators with the finite-element method (FEM) results in matrix systems that are solved with smoothed aggregation algebraic multigrid pre-conditioned conjugate gradient (AMG-PCG). After their initial setup, the AMG-PCG operators and coarse grid solvers are reused in each iteration step, further reducing computation time. The algorithm is tested on data from 23 surveys with a total of 6519 observation points in the Mt Isa–Cloncurry region in north–west Queensland, Australia. The mesh had about 2.5 million vertices and 16.5 million cells. A synthetic case was also tested using the same mesh and error measures for localized concentrations of high and low densities. The inversion results for different parameters are compared to each other as well as to lower order smoothing. Final inversion results are shown with and without depth weighting and compared to previous geological studies for the Mt Isa–Cloncurry region.
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46

Miller, S. M., A. M. Michalak, and P. J. Levi. "Atmospheric inverse modeling with known physical bounds: an example from trace gas emissions." Geoscientific Model Development 7, no. 1 (February 13, 2014): 303–15. http://dx.doi.org/10.5194/gmd-7-303-2014.

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Abstract. Many inverse problems in the atmospheric sciences involve parameters with known physical constraints. Examples include nonnegativity (e.g., emissions of some urban air pollutants) or upward limits implied by reaction or solubility constants. However, probabilistic inverse modeling approaches based on Gaussian assumptions cannot incorporate such bounds and thus often produce unrealistic results. The atmospheric literature lacks consensus on the best means to overcome this problem, and existing atmospheric studies rely on a limited number of the possible methods with little examination of the relative merits of each. This paper investigates the applicability of several approaches to bounded inverse problems. A common method of data transformations is found to unrealistically skew estimates for the examined example application. The method of Lagrange multipliers and two Markov chain Monte Carlo (MCMC) methods yield more realistic and accurate results. In general, the examined MCMC approaches produce the most realistic result but can require substantial computational time. Lagrange multipliers offer an appealing option for large, computationally intensive problems when exact uncertainty bounds are less central to the analysis. A synthetic data inversion of US anthropogenic methane emissions illustrates the strengths and weaknesses of each approach.
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47

de Groot‐Hedlin, Catherine, and Steven Constable. "Inversion of magnetotelluric data for 2D structure with sharp resistivity contrasts." GEOPHYSICS 69, no. 1 (January 2004): 78–86. http://dx.doi.org/10.1190/1.1649377.

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We have developed a linearized algorithm to invert noisy 2‐D magnetotelluric data for subsurface conductivity structures represented by smooth boundaries defining sharp resistivity contrasts. We solve for both a fixed number of subsurface resistivities and for the boundary locations between adjacent units. The boundary depths are forced to be discrete values defined by the mesh used in the forward modeling code. The algorithm employs a Lagrange multiplier approach in a manner similar to the widely used Occam method. The main difference is that we penalize variations in the boundary depths, rather than in resistivity contrasts between a large number of adjacent blocks. To reduce instabilities resulting from the breakdown of the linear approximation, we allow an option to penalize contrasts in the resistivities of adjacent units. We compare this boundary inversion method to the smooth Occam inversion for two synthetic models, one that includes a conductive wedge between two resistors and another that includes a resistive wedge between two conductors. The two methods give good agreement for the conductive wedge, but the solutions differ for the more poorly resolved resistive wedge, with the boundary inversion method giving a more geologically realistic result. Application of the boundary inversion method to the resistive Gemini subsalt petroleum prospect in the Gulf of Mexico indicates that the shape of this salt feature is accurately imaged by this method, and that the method remains stable when applied to real data.
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48

Carletti, Timoteo. "The lagrange inversion formula on non--Archimedean fields, non--analytical form of differential and finite difference equations." Discrete & Continuous Dynamical Systems - A 9, no. 4 (2003): 835–58. http://dx.doi.org/10.3934/dcds.2003.9.835.

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49

Scorpio, S. M., and R. F. Beck. "A Multipole Accelerated Desingularized Method for Computing Nonlinear Wave Forces on Bodies." Journal of Offshore Mechanics and Arctic Engineering 120, no. 2 (May 1, 1998): 71–76. http://dx.doi.org/10.1115/1.2829526.

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Nonlinear wave forces on offshore structures are investigated. The fluid motion is computed using a Euler-Lagrange time-domain approach. Nonlinear free surface boundary conditions are stepped forward in time using an accurate and stable integration technique. The field equation with mixed boundary conditions that result at each time step are solved at N nodes using a desingularized boundary integral method with multipole acceleration. Multipole accelerated solutions require O(N) computational effort and computer storage, while conventional solvers require O(N2) effort and storage for an iterative solution and O(N3) effort for direct inversion of the influence matrix. These methods are applied to the three-dimensional problem of wave diffraction by a vertical cylinder.
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50

Miller, S. M., A. M. Michalak, and P. J. Levi. "Atmospheric inverse modeling with known physical bounds: an example from trace gas emissions." Geoscientific Model Development Discussions 6, no. 3 (September 6, 2013): 4531–62. http://dx.doi.org/10.5194/gmdd-6-4531-2013.

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Abstract. Many inverse problems in the atmospheric sciences involve parameters with known physical constraints. Examples include non-negativity (e.g., emissions of some urban air pollutants) or upward limits implied by reaction or solubility constants. However, probabilistic inverse modeling approaches based on Gaussian assumptions cannot incorporate such bounds and thus often produce unrealistic results. The atmospheric literature lacks consensus on the best means to overcome this problem, and existing atmospheric studies rely on a limited number of the possible methods with little examination of the relative merits of each. This paper investigates the applicability of several approaches to bounded inverse problems and is also the first application of Markov chain Monte Carlo (MCMC) to estimation of atmospheric trace gas fluxes. The approaches discussed here are broadly applicable. A common method of data transformations is found to unrealistically skew estimates for the examined example application. The method of Lagrange multipliers and two MCMC methods yield more realistic and accurate results. In general, the examined MCMC approaches produce the most realistic result but can require substantial computational time. Lagrange multipliers offer an appealing alternative for large, computationally intensive problems when exact uncertainty bounds are less central to the analysis. A synthetic data inversion of US anthropogenic methane emissions illustrates the strengths and weaknesses of each approach.
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