1,720,996 research outputs found
A doubly relaxed minimal-norm Gauss–Newton method for underdetermined nonlinear least-squares problems
No full textWhen a physical system is modeled by a nonlinear function, the unknown parameters can be estimated by fitting experimental observations by a least-squares approach. Newton's method and its variants are often used to solve problems of this type. In this paper, we are concerned with the computation of the minimal-norm solution of an underdetermined nonlinear least-squares problem. We present a Gauss–Newton type method, which relies on two relaxation parameters to ensure convergence, and which incorporates a procedure to dynamically estimate the two parameters, as well as the rank of the Jacobian matrix, along the iterations. Numerical results are presented
La valutazione dei servizi ecosistemici culturali per i contesti bioregionali
No full textIl progetto bioregionale esprime una serie di sinergie atte al recupero degli equilibri ecologici, economici e socioculturali che hanno caratterizzato da sempre il rapporto tra territorio e comunità insediate (Magnaghi, 2014).
Nella valutazione dei metabolismi territoriali si confrontano due approcci distinti. Alcuni studiosi cercano di
esprimere un valore quantitativo e monetario degli ecosistemi alle diverse scale, integrando la dimensione ecologica a
quella economica e cercando di rendere tra loro comparabili i servizi offerti dall’ambiente naturale per il benessere
umano (Costanza, 2014). Altri mettono in primo piano la preminenza dell'etica e dell'estetica nella conservazione
degli ecosistemi, rifiutando qualsiasi tipo di contabilizzazione dei servizi ecosistemici, in quanto vista
concettualmente come un inaccettabile tentativo di mercificazione delle risorse naturali del pianeta (McCauley, 2006).
Ritenendo che i due approcci possano integrarsi vicendevolmente ed esprimere una loro complementarietà, il lavoro
proposto focalizza l’attenzione sulla valutazione quantitativa e qualitativa dei servizi ecosistemici culturali − CES, che
esprimono i valori intangibili e non monetizzabili degli ecosistemi, legati alla percezione dell’individuo e non
replicabili una volta degradati. I casi-studio analizzati si collocano nell’area metropolitana di Portland negli Stati Uniti.
La valutazione dei CES aspira a mettere in luce gli aspetti socio-culturali dei contesti bioregionali, ovvero quei valori
mediati dalla percezione e dalla memoria storico-culturale delle comunità che spesso sfuggono alle analisi degli
strumenti di piano tradizionali e pertanto non vengono tenuti in debita considerazione nei processi di policy making
A projection method for general form linear least-squares problems
Full text linkOne of the possible approaches for the solution of underdetermined linear least-squares problems in general form, for a chosen regularization operator L, projects the problem in the null space of L and in its orthogonal complement. In this paper, we show that the projected problem cannot be solved by the generalized singular value decomposition, and propose some approaches to overcome this issue. Numerical experiments ascertain the stability of the new procedures
Minimal-norm RKHS solution of an integral model in geo-electromagnetism
No full textIn this paper, a numerical method is developed for approximating the solution of a linear integral model in a reproducing kernel Hilbert space (RKHS). The model is typical of frequency domain electromagnetic (FDEM) induction methods in applied geophysics. The original problem is reformulated as a new one whose solution has the same smoothness properties as the original one. Then, the minimal-norm solution of such a model is computed through a numerical method that combines Riesz's theory with regularization tools. Several numerical tests illustrate the performance of the proposed approach
Color reconstruction by photometric stereo with unknown lighting of rock art carvings found in two Sardinian Domus de Janas
Full text linkArtifacts documentation is an important aspect of archaeological studies, not only to preserve these objects but also to learn from them the culture of ancient populations. Hence, the necessity to digitally document and archive artifacts that come from our ancestors. This work can be done with more ease for artifacts as vases, potsherds, or little handmade objects, that can be brought in a laboratory. It is more complicate for rock art carvings, that can not be moved from their original location. The photometric stereo technique allows to obtain the three-dimensional digital reconstruction of an object starting from a set of pictures taken with different lighting conditions. When the method is applied to some experimental datasets, computational problems may occur, due to the fact that some assumptions of the model are not verified: rocks are not Lambertian surfaces in general, and the light sources may not be positioned at a sufficient distance from the object. We deal with these issues by introducing numerical indicators of ideality that allow to figure out if a given dataset is reliable and which images should be selected to better reproduce the object. In this paper, we will show the application of this method to the 3D reconstruction of some engravings found in two Domus de Janas, ancient tombs located in Sardinia, Italy
Regularized minimal-norm solution of an overdetermined system of first kind integral equations
No full textOverdetermined systems of first kind integral equations appear in many applications. When the right-hand side is discretized, the resulting finite-data problem is ill-posed and admits infinitely many solutions. We propose a numerical method to compute the minimal-norm solution in the presence of boundary constraints. The algorithm stems from the Riesz representation theorem and operates in a reproducing kernel Hilbert space. Since the resulting linear system is strongly ill-conditioned, we construct a regularization method depending on a discrete parameter. It is based on the expansion of the minimal-norm solution in terms of the singular functions of the integral operator defining the problem. Two estimation techniques are tested for the automatic determination of the regularization parameter, namely, the discrepancy principle and the L-curve method. Numerical results concerning two artificial test problems demonstrate the excellent performance of the proposed method. Finally, a particular model typical of geophysical applications, which reproduces the readings of a frequency domain electromagnetic induction device, is investigated. The results show that the new method is extremely effective when the sought solution is smooth, but produces significant information even for non-smooth solutions
Linear Response Equations Revisited: A Simple and Efficient Iterative Algorithm
Full text linkWe present an algorithm to solve the linear response equations for Hartree-Fock, Density Functional Theory, and the Multiconfigurational Self-Consistent Field method that is both simple and efficient. The algorithm makes use of the well-established symmetric and antisymmetric combinations of trial vectors but further orthogonalizes them with respect to the scalar product induced by the response matrix. This leads to a standard, symmetric block eigenvalue problem in the expansion subspace that can be solved by diagonalizing a symmetric, positive definite matrix half the size of the expansion space. Numerical tests showed that the algorithm is robust and stable
An Efficient Implementation of the Gauss–Newton Method Via Generalized Krylov Subspaces
No full textThe solution of nonlinear inverse problems is a challenging task in numerical analysis. In most cases, this kind of problems is solved by iterative procedures that, at each iteration, linearize the problem in a neighborhood of the currently available approximation of the solution. The linearized problem is then solved by a direct or iterative method. Among this class of solution methods, the Gauss-Newton method is one of the most popular ones. We propose an efficient implementation of this method for large-scale problems. Our implementation is based on projecting the nonlinear problem into a sequence of nested subspaces, referred to as Generalized Krylov Subspaces, whose dimension increases with the number of iterations, except for when restarts are carried out. When the computation of the Jacobian matrix is expensive, we combine our iterative method with secant (Broyden) updates to further reduce the computational cost. We show convergence of the proposed solution methods and provide a few numerical examples that illustrate their performance
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
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