170,492 research outputs found
Numerical methods for large-scale Lyapunov equations with symmetric banded data
No full text<p>This Matlab code solves a large-scale Lyapunov matrix equation with SPD banded ill-conditioned coeff. matrix and banded right-hand side by the algorith called lyap_banded.</p>
<p>test_LB.m is an example of how to call the function Lyap_Banded.m.</p>
<p>The mex files TruncSubGen_mex.mexa64 and lowrank_normF.mexa64 are necessary when calling Lyap_Banded.m and they make use of LAPACK and C-BLAS subroutines.</p>
<p>The code does not include any checking of the input data.</p>
<p>Related manuscript:</p>
<p><a href="http://www.dm.unibo.it/~davide.palitta3/">Davide Palitta</a> and <a href="http://www.dm.unibo.it/~simoncin/">Valeria Simoncini</a><br>
NUMERICAL METHODS FOR LARGE-SCALE LYAPUNOV EQUATIONS WITH SYMMETRIC BANDED DATA<br>
To appear in SISC (<a href="https://arxiv.org/pdf/1711.04187.pdf">ArXiv: 1711.04187</a>) <br>
</p>
Computationally enhanced projection methods for symmetric Sylvester and Lyapunov matrix equations
No full text<p>These Matlab codes iteratively solve large-scale Sylvester and Lyapunov matrix equations with symmetric coeff. matrix by means of the standard Krylov method with Galerkin condition (low CPU and memory requirements). Version 1.0.</p>
<p>Computational routines for Lyapunov eqs: SKSM_cTri.m, cTri.mexa64</p>
<p>example_SKSM_cTri.m is an example of how to call the function SKSM_cTri.m. </p>
<p>Computational routines for Sylvester eqs: SKSM_Sylv_cTri.m, lapack.mexa64, eig_dstevr.m, tridiag_dsbtrd.m.</p>
<p>example_SKSM_Sylv_cTri.m is an example of how to call the function SKSM_Sylv_cTri.m.</p>
<p>Notice that the mex files cTri.mexa64 and lapack.mexa64 make use of LAPACK and C-BLAS subroutines.</p>
<p>The code does not include any checking of the input data.</p>
<p>Related manuscript:</p>
<p><a href="http://www.dm.unibo.it/~davide.palitta3/">Davide Palitta</a> and <a href="http://www.google.com/url?q=http%3A%2F%2Fwww.dm.unibo.it%2F~simoncin%2F&sa=D&sntz=1&usg=AFQjCNHmany7PkUC89gQ0bQw3k3wdrPYSQ">Valeria Simoncini</a>, <a href="http://www.google.com/url?q=http%3A%2F%2Fwww.sciencedirect.com%2Fscience%2Farticle%2Fpii%2FS0377042717304004%3Fvia%253Dihub&sa=D&sntz=1&usg=AFQjCNFUqbihWZvqNfC5Y0FIwopCgf3Nlw">Computationally enhanced projection methods for symmetric Sylvester and Lyapunov matrix equations</a>.</p>REMARK: A new version of this routines can be found at https://zenodo.org/record/3252320#.XUkybk5fhu
Evaluation of Friction at High Strain Rate using the Split Hopkinson Bar
No full textThe present work aims at studying the influence of strain rate on the frictional behaviour of AA7075 aluminium alloy in the O-annealed temper state. To this purpose, ring compression tests were performed both under quasi-static and dynamic loading conditions. The high strain rate tests were carried out by means of the Split Hopkinson Tension-Compression Bar in the direct version. In both cases, hollow cylindrical samples, characterised by an initial outer diameter to inner diameter to height ratio of 6:3:2, were tested under dry condition and by lubricating with molybdenum disulphide grease. The different frictional behaviour exhibited by AA7075-O under quasi-static and dynamic loading conditions can be attributed to the strain rate effect both on the plastic flow behaviour of the deformed material, and on the thickness of the lubricant film
On the decay of the inverse of matrices that are sum of Kronecker products
No full textDecay patterns of matrix inverses have recently attracted considerable interest, due to their relevance in numerical analysis, and in applications requiring matrix function approximations. In this paper we analyze the decay pattern of the inverse of banded matrices in the form , where M is tridiagonal, symmetric and positive definite, In is the identity matrix, and stands for the Kronecker product. It is well known that the inverses of banded matrices exhibit an exponential decay pattern away from the main diagonal. However, the entries in show a non- monotonic decay, which is not caught by classical bounds. By using an alternative expression for , we derive computable upper bounds that closely capture the actual behavior of its entries. We also show that similar estimates can be obtained when M has a larger bandwidth, or when the sum of Kronecker products involves two different matrices. Numerical experiments illustrating the new bounds are also reporte
Simulation of multipass hot rolling of AA 6082 aluminium alloy
No full textMultipass hot rolling of AA 6082 aluminium alloy were investigated by means of the simulative technique based on multistage hot torsion tests, performed on a hydraulically powered servo-controlled torsion machine. Three different test procedures, characterized by a linear decreasing temperature (from 525 to 300°C), a constant time between two subsequent deformations (20, 60 or 300 s) and a cumulative strain of 6.4 (number of passes equal to 16 or 32), were used: a) with constant strain rate on the specimen surface and constant strain per pass, b) with a linear increasing strain rate with a strain rate jump after each pass and constant strain per pass, c) with linear increasing strain rate and decreasing strain per pass. This allowed to simulate the rolling schedules for many combinations of process parameters. The influence of static and dynamic control parameters on the flow behaviour of the alloy was investigated in detail by analysing the flow curves. In particular, the envelope curves are influenced by the interpass time even if, at high temperatures, no significant effect is observed. The effect of the strain per pass differs from the one expected due to the strengthening effect produced by the static precipitation of second phase particles that is more enhanced as pass strain decreases. The strain rate path affects the envelope curves due to the strong influence of temperature on the constitutive parameters; finally, a more pronounced effect is produced by the strain path since early stages performed with larger pass strain values, owing to the more effectiveness of the dynamic restoration processes, lower the envelope curves
Approximate nonnegative matrix factorization algorithm for the analysis of angular differential imaging data
No full textThe angular differential imaging (ADI) is used to improve contrast in high resolution astronomical imaging. An example is the direct imaging of exoplanet in camera fed by Extreme Adaptive Optics. The subtraction of the main dazzling object to observe the faint companion was improved using Principal Component Analysis (PCA). It factorizes the positive astronomical frames into positive and negative components. On the contrary, the Nonnegative Matrix Factorization (NMF) uses only positive components, mimicking the actual composition of the long exposure images
Analysis of the rational Krylov subspace projection method for large-scale algebraic riccati equations
No full textIn the numerical solution of the algebraic Riccati equation A∗X + XA - XBB∗X + C∗C = 0, where A is large, sparse, and stable, and B, C have low rank, projection methods have recently emerged as a possible alternative to the more established Newton-Kleinman iteration. In spite of convincing numerical experiments, a systematic matrix analysis of this class of methods is still lacking. We derive new relations for the approximate solution, the residual, and the error matrices, giving new insights into the role of the matrix A - BB∗X and of its approximations in the numerical procedure. In the context of linear-quadratic regulator problems, we show that the Riccati approximate solution is related to the optimal value of the reduced cost functional, thus completely justifying the projection method from a model order reduction point of view. Finally, the new results provide theoretical ground for recently proposed modifications of projection methods onto rational Krylov subspaces
Computational methods for linear matrix equations
No full textGiven the square matrices A, B, D, E and the matrix C of conforming dimensions, we consider the linear matrix equation AXE + DXB = C in the unknown matrix X. Our aim is to provide an overview of the major algorithmic developments that have taken place over the past few decades in the numerical solution of this and related problems, which are producing reliable numerical tools in the formulation and solution of advanced mathematical models in engineering and scientific computing
Profili costituzionali della giurisprudenza europea sulla Brexit
No full textQuesto articolo si propone di comprendere come la giurisprudenza della Corte di giustizia sulla Brexit abbia interpretato la natura del rapporto che lega l’Unione europea (UE), gli Stati membri e i cittadini europei. Per quanto riguarda il rapporto dell’UE con gli Stati, la configurazione della revoca del recesso come diritto sovrano degli Stati nella sentenza Wightman determina alcuni rischi strategici per il funzionamento e il consolidamento del carattere sovranazionale dell’UE. Per quanto riguarda la cittadinanza europea, vengono analizzate le criticità del regime di tutela sia in termini di disponibilità di rimedi nella fase di negoziazione del recesso sia in materia di accesso ai benefici nel caso GC relativo al periodo di transizione
Contraction and Optimality Properties of an Adaptive Legendre–Galerkin Method: The Multi-Dimensional Case
No full textWe analyze the theoretical properties of an adaptive Legendre–Galerkin method in the multidimensional case. After the recent investigations for Fourier–Galerkin methods in a periodic box and for Legendre–Galerkin methods in the one dimensional setting, the present study represents a further step towards a mathematically rigorous understanding of adaptive spectral/hp discretizations of elliptic boundary-value problems. The main contribution of the paper is a careful construction of a multidimensional Riesz basis in H1, based on a quasi-orthonormalization procedure. This allows us to design an adaptive algorithm, to prove its convergence by a contraction argument, and to discuss its optimality properties (in the sense of non-linear approximation theory) in certain sparsity classes of Gevrey typ
- …
