| 971. |
- Burdakov, Oleg, 1953-, et al.
(författare)
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A generalised PAV algorithm for monotonic regression in several variables
- 2004
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Ingår i: COMPSTAT. Proceedings in Computational Statistics. - Heidelberg, NY : PhysicaVerlag/Springer. - 3790815543 ; , s. 761-767
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Konferensbidrag (refereegranskat)abstract
- We present a new algorithm for monotonic regression in one or more explanatory variables. Formally, our method generalises the well-known PAV (pool-adjacent-violators) algorithm from fully to partially ordered data. The computational complexity of our algorithm is O(n2). The goodness-of-fit to observed data is much closer to optimal than for simple averaging techniques.
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| 972. |
- Burdakov, Oleg, et al.
(författare)
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Regularized monotonic regression
- 2016
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- Monotonic (isotonic) Regression (MR) is a powerful tool used for solving a wide range of important applied problems. One of its features, which poses a limitation on its use in some areas, is that it produces a piecewise constant fitted response. For smoothing the fitted response, we introduce a regularization term in the MR formulated as a least distance problem with monotonicity constraints. The resulting Smoothed Monotonic Regrassion (SMR) is a convex quadratic optimization problem. We focus on the SMR, where the set of observations is completely (linearly) ordered. Our Smoothed Pool-Adjacent-Violators (SPAV) algorithm is designed for solving the SMR. It belongs to the class of dual activeset algorithms. We proved its finite convergence to the optimal solution in, at most, n iterations, where n is the problem size. One of its advantages is that the active set is progressively enlarging by including one or, typically, more constraints per iteration. This resulted in solving large-scale SMR test problems in a few iterations, whereas the size of that problems was prohibitively too large for the conventional quadratic optimization solvers. Although the complexity of the SPAV algorithm is O(n2), its running time was growing in our computational experiments in proportion to n1:16.
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| 973. |
- Burman, Erik, et al.
(författare)
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A cut finite element method for elliptic bulk problems with embedded surfaces
- 2019
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Ingår i: GEM - International Journal on Geomathematics. - : Springer. - 1869-2672 .- 1869-2680. ; 10:1
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Tidskriftsartikel (refereegranskat)abstract
- We propose an unfitted finite element method for flow in fractured porous media. The coupling across the fracture uses a Nitsche type mortaring, allowing for an accurate representation of the jump in the normal component of the gradient of the discrete solution across the fracture. The flow field in the fracture is modelled simultaneously, using the average of traces of the bulk variables on the fractures. In particular the Laplace–Beltrami operator for the transport in the fracture is included using the average of the projection on the tangential plane of the fracture of the trace of the bulk gradient. Optimal order error estimates are proven under suitable regularity assumptions on the domain geometry. The extension to the case of bifurcating fractures is discussed. Finally the theory is illustrated by a series of numerical examples.
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| 974. |
- Börlin, Niclas, 1968-, et al.
(författare)
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Efficient computation of posterior covariance in bundle adjustment in DBAT for projects with large number of object points
- 2020
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Ingår i: XXIV ISPRS Congress. - : International Society for Photogrammetry and Remote Sensing (ISPRS). ; , s. 737-744
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Konferensbidrag (refereegranskat)abstract
- One of the major quality control parameters in bundle adjustment arethe posterior estimates of the covariance of the estimated parameters. Posterior covariance computations have been part of the open source Damped Bundle Adjustment Toolbox in Matlab (DBAT) since its first public release. However, for large projects, the computation of especially the posterior covariances of object points have been time consuming.The non-zero structure of the normal matrix depends on the ordering of the parameters to be estimated. For some algorithms, the ordering of the parameters highly affect the computational effort needed to compute the results. If the parameters are ordered to have the object points first, the non-zero structure of the normal matrix forms an arrowhead.In this paper, the legacy DBAT posterior computation algorithm was compared to three other algorithms: The Classic algorithm based on the reduced normal equation, the Sparse Inverse algorithm by Takahashi, and the novel Inverse Cholesky algorithm. The Inverse Cholesky algorithm computes the explicit inverse of the Cholesky factor of the normal matrix in arrowhead ordering.The algorithms were applied to normal matrices of ten data sets of different types and sizes. The project sizes ranged from 21 images and 100 object points to over 900 images and 400,000 object points. Both self-calibration and non-self-calibration cases were investigated. The results suggest that the Inverse Cholesky algorithm is the fastest for projects up to about 300 images. For larger projects, the Classic algorithm is faster. Compared to the legacy DBAT implementation, the Inverse Cholesky algorithm provides a performance increase by one to two orders of magnitude. The largest data set was processed in about three minutes on a five year old workstation.The legacy and Inverse Cholesky algorithms were implemented in Matlab. The Classic and Sparse Inverse algorithms included codes written in C. For a general toolbox as DBAT, a pure Matlab implementation is advantageous, as it removes any dependencies on,e.g., compilers. However, for a specific lab with mostly large projects, compiling and using the classic algorithm will give improved performance. Nevertheless, the Inverse Cholesky algorithm is a significant addition to DBAT as it enables a relatively rapid computation of more statistical metrics, further reinforcing its application for reprocessing bundle adjustment results of black-box solutions.
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| 975. |
- Börlin, Niclas, 1968-, et al.
(författare)
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Flexible Photogrammetric Computations Using Modular Bundle Adjustment : The Chain Rule and the Collinearity Equations
- 2019
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Ingår i: Photogrammetric Engineering and Remote Sensing. - Bethesda, Maryland, USA : American Society of Photogrammetry and Remote Sensing (ASPRS). - 0099-1112. ; 85:5, s. 361-368
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Tidskriftsartikel (refereegranskat)abstract
- The main purpose of this article is to show that photogrammetric bundle-adjustment computations can be sequentially organized into modules. Furthermore, the chain rule can be used to simplify the computation of the analytical Jacobians needed for the adjustment. Novel projection models can be flexibly evaluated by inserting, modifying, or swapping the order of selected modules. As a proof of concept, two variants of the pinhole projection model with Brown lens distortion were implemented in the open-source Damped Bundle Adjustment Toolbox and applied to simulated and calibration data for a nonconventional lens system. The results show a significant difference for the simulated, error-free, data but not for the real calibration data. The current flexible implementation incurs a performance loss. However, in cases where flexibility is more important, the modular formulation should be a useful tool to investigate novel sensors, data-processing techniques, and refractive models.
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| 976. |
- Börlin, Niclas, 1968-, et al.
(författare)
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Modular Bundle Adjustment for Photogrammeric Computations
- 2018
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Ingår i: ISPRS Technical Commission II Symposium 2018. - : ISPRS. ; , s. 133-140
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Konferensbidrag (refereegranskat)abstract
- In this paper we investigate how the residuals in bundle adjustmentcan be split into a composition of simple functions. According to thechain rule, the Jacobian (linearisation) of the residual can be formedas a product of the Jacobians of the individual steps. Whenimplemented, this enables a modularisation of the computation of thebundle adjustment residuals and Jacobians where each component haslimited responsibility. This enables simple replacement of componentsto e.g. implement different projection or rotation models byexchanging a module. The technique has previously been used toimplement bundle adjustment in the open-source package DBAT (Borlinand Grussenmeyer, ¨ 2013) based on the Photogrammetric and ComputerVision interpretations of Brown (1971) lens distortion model. In thispaper, we applied the technique to investigate how affine distortionscan be used to model the projection of a tilt-shift lens. Two extendeddistortion models were implemented to test the hypothesis that theordering of the affine and lens distortion steps can be changed toreduce the size of the residuals of a tilt-shift lens calibration.Results on synthetic data confirm that the ordering of the affine andlens distortion steps matter and is detectable by DBAT. However, whenapplied to a real camera calibration data set of a tilt-shift lens, nodifference between the extended models was seen. This suggests thatthe tested hypothesis is false and that other effects need to bemodelled to better explain the projection. The relatively lowimplementation effort that was needed to generate the models suggestthat the technique can be used to investigate other novel projectionmodels in photogrammetry, including modelling changes in the 3Dgeometry to better understand the tilt-shift lens.
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| 977. |
- Calogero, Simone, 1974
(författare)
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On Self-Gravitating Polytropic Elastic Balls
- 2022
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Ingår i: Annales Henri Poincare. - : Springer Science and Business Media LLC. - 1424-0637 .- 1424-0661. ; 23
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Tidskriftsartikel (refereegranskat)abstract
- A new four-parameters family of constitutive functions for spherically symmetric elastic bodies is introduced which extends the two-parameters class of polytropic fluid models widely used in several applications of fluid mechanics. The four parameters in the polytropic elastic model are the polytropic exponent gamma, the bulk modulus kappa, the shear exponent beta and the Poisson ratio nu is an element of (-1,1/2]. The two-parameters class of polytropic fluid models arises as a special case when nu = 1/2 and beta = gamma. In contrast to the standard Lagrangian approach to elasticity theory, the polytropic elastic model in this paper is formulated directly in physical space, i.e., in terms of Eulerian state variables, which is particularly useful for the applications, e.g., to astrophysics where the reference state of the bodies of interest (stars, planets, etc.) is not observable. After discussing some general properties of the polytropic elastic model, the steady states and the homologous motion of Newtonian self-gravitating polytropic elastic balls are investigated. It is shown numerically that static balls exist when the parameters gamma, beta are contained in a particular region O of the plane, depending on nu, and proved analytically for (gamma, beta) is an element of nu, where nu subset of O is a disconnected set which also depends on the Poisson ratio nu. Homologous solutions describing continuously collapsing balls are constructed numerically when gamma = 4/3. The radius of these solutions shrinks to zero in finite time, causing the formation of a center singularity with infinite density and pressure. Expanding self-gravitating homologous elastic balls are also constructed analytically for some special values of the shear parameter beta.
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| 978. |
- Canhanga, Betuel, 1980-, et al.
(författare)
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Analytical and Numerical Studies on the Second Order Asymptotic Expansion Method for European Option Pricing under Two-factor Stochastic Volatilities
- 2018
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Ingår i: Communications in Statistics - Theory and Methods. - : Taylor & Francis. - 0361-0926 .- 1532-415X. ; 47:6, s. 1328-1349
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Tidskriftsartikel (refereegranskat)abstract
- The celebrated Black–Scholes model made the assumption of constant volatility but empirical studies on implied volatility and asset dynamics motivated the use of stochastic volatilities. Christoffersen in 2009 showed that multi-factor stochastic volatilities models capture the asset dynamics more realistically. Fouque in 2012 used it to price European options. In 2013 Chiarella and Ziveyi considered Christoffersen's ideas and introduced an asset dynamics where the two volatilities of the Heston type act separately and independently on the asset price, and using Fourier transform for the asset price process and double Laplace transform for the two volatilities processes, solved a pricing problem for American options. This paper considers the Chiarella and Ziveyi model and parameterizes it so that the volatilities revert to the long-run-mean with reversion rates that mimic fast(for example daily) and slow(for example seasonal) random effects. Applying asymptotic expansion method presented by Fouque in 2012, we make an extensive and detailed derivation of the approximation prices for European options. We also present numerical studies on the behavior and accuracy of our first and the second order asymptotic expansion formulas.
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| 979. |
- Carling, Kenneth, et al.
(författare)
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Confidence in heuristic solutions?
- 2015
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Ingår i: Journal of Global Optimization. - : Springer Science and Business Media LLC. - 0925-5001 .- 1573-2916. ; 63:2, s. 381-399
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Tidskriftsartikel (refereegranskat)abstract
- Solutions to combinatorial optimization problems frequently rely on heuristics to minimize an objective function. The optimum is sought iteratively and pre-setting the number of iterations dominates in operations research applications, which implies that the quality of the solution cannot be ascertained. Deterministic bounds offer a mean of ascertaining the quality, but such bounds are available for only a limited number of heuristics and the length of the interval may be difficult to control in an application. A small, almost dormant, branch of the literature suggests using statistical principles to derive statistical bounds for the optimum. We discuss alternative approaches to derive statistical bounds. We also assess their performance by testing them on 40 test p-median problems on facility location, taken from Beasley’s OR-library, for which the optimum is known. We consider three popular heuristics for solving such location problems; simulated annealing, vertex substitution, and Lagrangian relaxation where only the last offers deterministic bounds. Moreover, we illustrate statistical bounds in the location of 71 regional delivery points of the Swedish Post. We find statistical bounds reliable and much more efficient than deterministic bounds provided that the heuristic solutions are sampled close to the optimum. Statistical bounds are also found computationally affordable.
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| 980. |
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