Related papers: Least-squares for linear elasticity eigenvalue pro…
The spectrum of the Laplace-Beltrami operator, computed on the spatial slices of Causal Dynamical Triangulations, is a powerful probe of the geometrical properties of the configurations sampled in the various phases of the lattice theory.…
Eigenvalue spectrum has been a long term unsolved problem for plasma physicists. In this paper, some numerical calculations are conducted about the minimum eigenvalues of the linearized Rosenbluth collision operator and the differential…
Based on a potential theoretical approach, the subsurface stress field is calculated for an elastic-half space, which is subject to normal and uniaxial tangential surface tractions that - in the case of elastic decoupling - correspond to…
In this work we introduce novel stress-only formulations of linear elasticity with special attention to their approximate solution using weighted residual methods. We present four sets of boundary value problems for a pure stress…
A multiple interval-valued linear regression model considering all the cross-relationships between the mids and spreads of the intervals has been introduced recently. A least-squares estimation of the regression parameters has been carried…
We define and analyse a least-squares finite element method for a first-order reformulation of the obstacle problem. Moreover, we derive variational inequalities that are based on similar but non-symmetric bilinear forms. A priori error…
This paper is concerned with the least squares estimator for a basic class of nonlinear autoregressive models, whose outputs are not necessarily to be ergodic. Several asymptotic properties of the least squares estimator have been…
We consider the linear least squares problem with linear equality constraints (LSE problem) formulated as $\min_{x\in\mathbb{R}^{n}}\|Ax-b\|_2 \ \mathrm{s.t.} \ Cx = d$. Although there are some classical methods available to solve this…
This paper is concerned with the design and analysis of a fully adaptive eigenvalue solver for linear symmetric operators. After transforming the original problem into an equivalent one formulated on $\ell_2$, the space of square summable…
It is shown that when the well-known minimal complementary energy variational principle in linear elastostatics is written in a different form with the strain tensor as an independent variable and the constitutive relation as one of the…
Calculating by analytical theory the deformation of finite-sized elastic bodies in response to internally applied forces is a challenge. Here, we derive explicit analytical expressions for the amplitudes of modes of surface deformation of a…
Nowadays, Non-Linear Least-Squares embodies the foundation of many Robotics and Computer Vision systems. The research community deeply investigated this topic in the last years, and this resulted in the development of several open-source…
We present a variational characterization of mechanical equilibrium in the planar strain regime for systems with incompatible kinematics. For non-simply connected domains, we show that the equilibrium problem for a non-liftable…
We study the low-lying spectrum of the Dirichlet Laplace operator on a randomly wiggled strip. More precisely, our results are formulated in terms of the eigenvalues of finite segment approximations of the infinite waveguide. Under…
In this paper, we address the accuracy of the results for the overdetermined full rank linear least squares problem. We recall theoretical results obtained in Arioli, Baboulin and Gratton, SIMAX 29(2):413--433, 2007, on conditioning of the…
The use of global displacement basis functions to solve boundary-value problems in linear elasticity is well established. No prior work uses a global stress tensor basis for such solutions. We present two such methods for solving stress…
We address the phase retrieval problem with errors in the sensing vectors. A number of recent methods for phase retrieval are based on least squares (LS) formulations which assume errors in the quadratic measurements. We extend this…
We consider the elasticity operator with zero Poisson's ratio on an infinite strip and an infinite plate with a horizontal crack. We prove an asymptotic formula for the distance of the embedded eigenvalues to some spectral threshold of the…
We give sparsity results and present algorithms for calculating minimum (vector) 1-norm universal solvers connected to least-squares problems. In particular, besides universal least-squares solvers, we consider minimum-rank universal…
The linear response of two-dimensional amorphous elastic bodies to an external delta force is determined in analogy with recent experiments on granular aggregates. For the generated forces, stress and displacement fields, we find strong…