Generalized locally Toeplitz sequences : Theory and applications

[1]  T. Hughes,et al.  Efficient quadrature for NURBS-based isogeometric analysis , 2010 .

[2]  Imanol Perez Arribas.  Sobolev Spaces and Partial Differential Equations , 2017 .

[3]  H. Widom.  Extreme eigenvalues of translation kernels , 1961 .

[4]  Paolo Tilli,et al.  A note on the spectral distribution of toeplitz matrices , 1998 .

[5]  E. E. Tyrtyshnikov.  A unifying approach to some old and new theorems on distribution and clustering , 1996 .

[6]  Hendrik Speleers,et al.  Robust and optimal multi-iterative techniques for IgA Galerkin linear systems This is a preprint of a paper published in Comput. Methods Appl. Mech. Engrg. 284 (2015) 230264. , 2015 .

[7]  Paolo Tilli,et al.  Locally Toeplitz sequences: spectral properties and applications , 1998 .

[8]  Amara Lynn Graps,et al.  An introduction to wavelets , 1995 .

[9]  Albrecht Böttcher,et al.  Spectral properties of banded Toeplitz matrices , 1987 .

[10]  Carl de Boor,et al.  A Practical Guide to Splines , 1978, Applied Mathematical Sciences.

[11]  Paolo Tilli,et al.  On unitarily invariant norms of matrix-valued linear positive operators , 2002 .

[12]  Milutin R. Dostanić,et al.  On the distribution singular values of Toeplitz matrices , 2001 .

[13]  Federico Poloni,et al.  An effective matrix geometric mean satisfying the Ando-Li-Mathias properties , 2010, Math. Comput..

[14]  Hendrik Speleers,et al.  Lusin theorem, GLT sequences and matrix computations: An application to the spectral analysis of PDE discretization matrices , 2017 .

[15]  Stefano Serra Capizzano,et al.  On the Asymptotic Spectrum of Finite Element Matrix Sequences , 2007, SIAM J. Numer. Anal..

[16]  S. Serra Capizzano,et al.  Generalized locally Toeplitz sequences: spectral analysis and applications to discretized partial differential equations , 2003 .

[17]  Paolo Tilli,et al.  Asymptotic Spectra of Hermitian Block Toeplitz Matrices and Preconditioning Results , 2000, SIAM J. Matrix Anal. Appl..

[18]  O. Zabroda.  Generalized convolution operators and asymptotic spectral theory , 2006 .

[19]  F. Avram.  On bilinear forms in Gaussian random variables and Toeplitz matrices , 1988 .

[20]  Asymptotic Behavior of Variable-Coefficient Toeplitz Determinants , 2001 .

[21]  Gene H. Golub,et al.  Numerical solution of saddle point problems , 2005, Acta Numerica.

[22]  Stefano Serra Capizzano,et al.  Asymptotic Zero Distribution of Orthogonal Polynomials with Discontinuously Varying Recurrence Coefficients , 2001, J. Approx. Theory.

[23]  Arno B. J. Kuijlaars,et al.  Superlinear Convergence of Conjugate Gradients , 2001, SIAM J. Numer. Anal..

[24]  Frederic Barbaresco,et al.  Robust statistical Radar Processing in Fréchet metric space: OS-HDR-CFAR and OS-STAP Processing in Siegel homogeneous bounded domains , 2011, 2011 12th International Radar Symposium (IRS).

[25]  R. Bhatia,et al.  Riemannian geometry and matrix geometric means , 2006 .

[26]  H. Widom,et al.  From Toeplitz Eigenvalues through Green’s Kernels to Higher-order Wirtinger-Sobolev Inequalities , 2004, math/0412269.

[27]  A. Böttcher,et al.  Introduction to Large Truncated Toeplitz Matrices , 1998 .

[28]  Ben Jeuris,et al.  A survey and comparison of contemporary algorithms for computing the matrix geometric mean , 2012 .

[29]  Stefano Serra Capizzano,et al.  Spectral behavior of preconditioned non-Hermitian multilevel block Toeplitz matrices with matrix-valued symbol , 2014, Appl. Math. Comput..

[30]  Arno B. J. Kuijlaars,et al.  The Asymptotic Zero Distribution of Orthogonal Polynomials with Varying Recurrence Coefficients , 1999 .

[31]  B. Silbermann,et al.  Sequences of variable-coefficient Toeplitz matrices and their singular values , 2016 .

[32]  Stefano Serra,et al.  On the extreme spectral properties of Toeplitz matrices generated byL1 functions with several minima/maxima , 1996 .

[33]  S. Serra-Capizzano,et al.  The theory of generalized locally Toeplitz sequences : a review, an extension, and a few representative applications , 2017 .

[34]  D. Fasino,et al.  From Toeplitz matrix sequences to zero distribution of orthogonal polynomials , 2001 .

[35]  Hendrik Speleers,et al.  Spectral analysis and spectral symbol of matrices in isogeometric Galerkin methods , 2017, Math. Comput..

[36]  Marco Donatelli,et al.  Canonical Eigenvalue Distribution of Multilevel Block Toeplitz Sequences with Non-Hermitian Symbols , 2012 .

[37]  Stefano Serra Capizzano,et al.  Singular‐value (and eigenvalue) distribution and Krylov preconditioning of sequences of sampling matrices approximating integral operators , 2014, Numer. Linear Algebra Appl..

[38]  Stefano Serra,et al.  On the extreme eigenvalues of hermitian (block) toeplitz matrices , 1998 .

[39]  Debora Sesana.  Spectral distributions of structured matrix-sequences: tools and applications. , 2011 .

[40]  Eugene E. Tyrtyshnikov,et al.  Spectra of multilevel toeplitz matrices: Advanced theory via simple matrix relationships , 1998 .

[41]  Carlo Garoni.  Structured matrices coming from PDE approximation theory: spectral analysis, spectral symbol and design of fast iterative solvers. , 2015 .

[42]  F. Barbaresco,et al.  Radar detection using Siegel distance between autoregressive processes, application to HF and X-band radar , 2008, 2008 IEEE Radar Conference.

[43]  Toeplitz matrices with variable coefficients, pseudodifferential operators, and Strichartz's method , 2010 .

[44]  Alessandro Reali,et al.  Duality and unified analysis of discrete approximations in structural dynamics and wave propagation : Comparison of p-method finite elements with k-method NURBS , 2008 .

[45]  Paolo Tilli,et al.  Some Results on Complex Toeplitz Eigenvalues , 1999 .

[46]  Estimates for the minimum eigenvalue and the condition number of Hermitian (block) Toeplitz matrices , 2013 .

[47]  R. Karandikar,et al.  Monotonicity of the matrix geometric mean , 2012 .

[48]  Alessandro Reali,et al.  Isogeometric collocation: Cost comparison with Galerkin methods and extension to adaptive hierarchical NURBS discretizations , 2013 .

[49]  S. Serra Capizzano,et al.  Distribution results on the algebra generated by Toeplitz sequences: a finite-dimensional approach , 2001 .

[50]  Stefano Serra Capizzano,et al.  Analysis of preconditioning strategies for collocation linear systems , 2003 .

[51]  S. Serra-Capizzano,et al.  Approximating classes of sequences: The Hermitian case , 2011 .

[52]  W. Rudin.  Real and complex analysis , 1968 .

[53]  Stefano Serra-Capizzano,et al.  The eigenvalue distribution of products of Toeplitz matrices – Clustering and attraction , 2010 .

[54]  A. Böttcher,et al.  Uniform Boundedness of Toeplitz Matrices with Variable Coefficients , 2008 .

[55]  Carlo Garoni,et al.  A general tool for determining the asymptotic spectral distribution of Hermitian matrix-sequences , 2015 .

[56]  Noboru Nakamura,et al.  Geometric Means of Positive Operators , 2009 .

[57]  Alessandro Reali,et al.  Finite element and NURBS approximations of eigenvalue, boundary-value, and initial-value problems , 2014 .

[58]  Alessandro Reali,et al.  Isogeometric Analysis of Structural Vibrations , 2006 .

[59]  Dario Andrea Bini,et al.  Metodi Numerici per l'Algebra Lineare. , 1989 .

[60]  F. Barbaresco.  Information Geometry of Covariance Matrix: Cartan-Siegel Homogeneous Bounded Domains, Mostow/Berger Fibration and Fréchet Median , 2013 .

[61]  Thomas J. R. Hughes,et al.  Isogeometric Analysis: Toward Integration of CAD and FEA , 2009 .

[62]  Alessandro Reali,et al.  AN ISO GEOMETRIC ANALYSIS APPROACH FOR THE STUDY OF STRUCTURAL VIBRATIONS , 2006 .

[63]  U. Grenander,et al.  Toeplitz Forms And Their Applications , 1958 .

[64]  L. Hörmander,et al.  Pseudo-differential Operators and Non-elliptic Boundary Problems , 1966 .

[65]  Stefano Serra-Capizzano,et al.  Stability of the notion of approximating class of sequences and applications , 2008 .

[66]  T. Hughes,et al.  ISOGEOMETRIC COLLOCATION METHODS , 2010 .

[67]  Maya Neytcheva,et al.  Spectral analysis of coupled PDEs and of their Schur complements via the notion of generalized locally Toeplitz sequences , 2015 .

[68]  Hendrik Speleers,et al.  Robust and optimal multi-iterative techniques for IgA Galerkin linear systems , 2015 .

[69]  Carlo Garoni,et al.  Tools for Determining the Asymptotic Spectral Distribution of non-Hermitian Perturbations of Hermitian Matrix-Sequences and Applications , 2015 .

[70]  Pedro M. Crespo,et al.  Mass concentration in quasicommutators of Toeplitz matrices , 2007 .

[71]  Stefano Serra-Capizzano.  More Inequalities and Asymptotics for Matrix Valued Linear Positive Operators: the Noncommutative Case , 2002 .

[72]  A. Böttcher,et al.  Variable-coefficient Toeplitz Matrices with Symbols beyond the Wiener Algebra , 2010 .

[73]  Carlo Garoni,et al.  Spectral Analysis and Spectral Symbol of d-variate $\mathbb Q_{\boldsymbol p}$ Lagrangian FEM Stiffness Matrices , 2015, SIAM J. Matrix Anal. Appl..

[74]  A. Böttcher,et al.  On the condition numbers of large semidefinite Toeplitz matrices , 1998 .

[75]  T. Hughes,et al.  Isogeometric analysis : CAD, finite elements, NURBS, exact geometry and mesh refinement , 2005 .

[76]  Stefano Serra-Capizzano,et al.  The GLT class as a generalized Fourier analysis and applications , 2006 .

[77]  Szego-Type Limit Theorems for Generalized Discrete Convolution Operators , 2005 .

[78]  R. Bhatia.  Positive Definite Matrices , 2007 .

[79]  Bernd Silbermann,et al.  Asymptotic Behavior of Generalized Convolutions: An Algebraic Approach , 2006 .

[80]  Hendrik Speleers,et al.  Symbol-Based Multigrid Methods for Galerkin B-Spline Isogeometric Analysis , 2017, SIAM J. Numer. Anal..

[81]  Stefano Serra-Capizzano,et al.  Eigenvalue-eigenvector structure of Schoenmakers–Coffey matrices via Toeplitz technology and applications , 2016 .

[82]  A. Quarteroni.  Numerical Models for Differential Problems , 2009 .

[83]  G. Smith,et al.  Numerical Solution of Partial Differential Equations: Finite Difference Methods , 1978 .

[84]  Hendrik Speleers,et al.  On the spectrum of stiffness matrices arising from isogeometric analysis , 2014, Numerische Mathematik.

[85]  Dario Bini,et al.  Computing the Karcher mean of symmetric positive definite matrices , 2013 .

[86]  Seymour V. Parter,et al.  On the extreme eigenvalues of Toeplitz matrices , 1961 .

[87]  Leonid Golinskii,et al.  The asymptotic properties of the spectrum of nonsymmetrically perturbed Jacobi matrix sequences , 2007, J. Approx. Theory.

[88]  Y. Lim,et al.  Monotonic properties of the least squares mean , 2010, 1007.4792.

[89]  A. Böttcher,et al.  Toeplitz Matrices, Asymptotic Linear Algebra, and Functional Analysis , 2000 .