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Journal articles on the topic 'Spectral convergence'

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Published: 30 May 2022
Last updated: 31 May 2022

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1

Deitmar, Anton. "Benjamini–Schramm and spectral convergence." L’Enseignement Mathématique 64, no. 3 (July 23, 2019): 371–94. http://dx.doi.org/10.4171/lem/64-3/4-8.

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2

Kasue, Atsushi, and Hironori Kumura. "Spectral convergence of Riemannian manifolds." Tohoku Mathematical Journal 46, no. 2 (1994): 147–79. http://dx.doi.org/10.2748/tmj/1178225756.

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3

Buhmann, Martin, and Nira Dyn. "Spectral convergence of multiquadric interpolation." Proceedings of the Edinburgh Mathematical Society 36, no. 2 (June 1993): 319–33. http://dx.doi.org/10.1017/s0013091500018411.

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In this paper, we consider interpolants on h·ℤn from the closure of the space spanned by translates of the function (‖·‖2 + 1)β/2 (β>−n and not an even nonnegative integer) along h·ℤn. We show that these interpolants approximate a function, whose Fourier transform satisfies certain asymptotic conditions, up to an error of order hp, on any compact domain in ℝn, where p is only restricted by the smoothness of the function.
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4

Ji, Lizhen, and Richard Wentworth. "Spectral convergence on degenerating surfaces." Duke Mathematical Journal 66, no. 3 (June 1992): 469–501. http://dx.doi.org/10.1215/s0012-7094-92-06615-4.

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5

Sánchez-Perales, Salvador, and Slaviša V. Djordjević. "Spectral continuity using ν-convergence." Journal of Mathematical Analysis and Applications 433, no. 1 (January 2016): 405–15. http://dx.doi.org/10.1016/j.jmaa.2015.07.069.

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6

Kasue, Atsushi, and Hironori Kumura. "Spectral convergence of Riemannian manifolds, II." Tohoku Mathematical Journal 48, no. 1 (1996): 71–120. http://dx.doi.org/10.2748/tmj/1178225413.

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7

BECKUS, SIEGFRIED, and FELIX POGORZELSKI. "Delone dynamical systems and spectral convergence." Ergodic Theory and Dynamical Systems 40, no. 6 (October 22, 2018): 1510–44. http://dx.doi.org/10.1017/etds.2018.116.

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In the realm of Delone sets in locally compact, second countable Hausdorff groups, we develop a dynamical systems approach in order to study the continuity behavior of measured quantities arising from point sets. A special focus is both on the autocorrelation, as well as on the density of states for random bounded operators. It is shown that for uniquely ergodic limit systems, the latter measures behave continuously with respect to the Chabauty–Fell convergence of hulls. In the special situation of Euclidean spaces, our results complement recent developments in describing spectra as topological limits: we show that the measured quantities under consideration can be approximated via periodic analogs.
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8

Rowlett, Julie. "Spectral geometry and asymptotically conic convergence." Communications in Analysis and Geometry 16, no. 4 (2008): 735–98. http://dx.doi.org/10.4310/cag.2008.v16.n4.a2.

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9

Mohammadi, M., and R. Schaback. "Convergence analysis of general spectral methods." Journal of Computational and Applied Mathematics 313 (March 2017): 284–93. http://dx.doi.org/10.1016/j.cam.2016.09.031.

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10

Honda, Shouhei. "Spectral convergence under bounded Ricci curvature." Journal of Functional Analysis 273, no. 5 (September 2017): 1577–662. http://dx.doi.org/10.1016/j.jfa.2017.05.009.

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11

Kremling, Gitte, and Robert Speck. "Convergence of multilevel spectral deferred corrections." Communications in Applied Mathematics and Computational Science 16, no. 2 (November 2, 2021): 227–65. http://dx.doi.org/10.2140/camcos.2021.16.227.

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12

Bellavia, Stefania, Nataša Krklec Jerinkić, and Greta Malaspina. "Subsampled Nonmonotone Spectral Gradient Methods." Communications in Applied and Industrial Mathematics 11, no. 1 (January 1, 2020): 19–34. http://dx.doi.org/10.2478/caim-2020-0002.

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AbstractThis paper deals with subsampled spectral gradient methods for minimizing finite sums. Subsample function and gradient approximations are employed in order to reduce the overall computational cost of the classical spectral gradient methods. The global convergence is enforced by a nonmonotone line search procedure. Global convergence is proved provided that functions and gradients are approximated with increasing accuracy. R-linear convergence and worst-case iteration complexity is investigated in case of strongly convex objective function. Numerical results on well known binary classification problems are given to show the effectiveness of this framework and analyze the effect of different spectral coefficient approximations arising from the variable sample nature of this procedure.
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13

Hu, P., I. Kriz, and K. Ormsby. "Convergence of the Motivic Adams Spectral Sequence." Journal of K-theory 7, no. 3 (April 11, 2011): 573–96. http://dx.doi.org/10.1017/is011003012jkt150.

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AbstractWe prove convergence of the motivic Adams spectral sequence to completions at p and η under suitable conditions. We also discuss further conditions under which η can be removed from the statement.
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14

Ji, Lizhen, and Richard Wentworth. "Correction to ?Spectral convergence on degenerating surfaces?" Duke Mathematical Journal 90, no. 1 (October 1997): 205–7. http://dx.doi.org/10.1215/s0012-7094-97-09007-4.

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15

E, Weinan. "Convergence of Spectral Methods for Burgers’ Equation." SIAM Journal on Numerical Analysis 29, no. 6 (December 1992): 1520–41. http://dx.doi.org/10.1137/0729088.

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16

Futaki, Akito, Shouhei Honda, and Shunsuke Saito. "Fano–Ricci limit spaces and spectral convergence." Asian Journal of Mathematics 21, no. 6 (2017): 1015–62. http://dx.doi.org/10.4310/ajm.2017.v21.n6.a2.

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17

Lomov, I. S. "Loaded differential operators: Convergence of spectral expansions." Differential Equations 50, no. 8 (August 2014): 1070–79. http://dx.doi.org/10.1134/s0012266114080060.

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18

Post, Olaf. "Spectral Convergence of Quasi-One-Dimensional Spaces." Annales Henri Poincaré 7, no. 5 (August 2006): 933–73. http://dx.doi.org/10.1007/s00023-006-0272-x.

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19

Öffner, Philipp, and Thomas Sonar. "Spectral convergence for orthogonal polynomials on triangles." Numerische Mathematik 124, no. 4 (February 26, 2013): 701–21. http://dx.doi.org/10.1007/s00211-013-0530-z.

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20

Kollnig, Konrad, Paolo Bientinesi, and Edoardo A. Di Napoli. "Rational Spectral Filters with Optimal Convergence Rate." SIAM Journal on Scientific Computing 43, no. 4 (January 2021): A2660—A2684. http://dx.doi.org/10.1137/20m1313933.

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21

Lebeau, Gilles, and Laurent Michel. "SPECTRAL ANALYSIS OF HYPOELLIPTIC RANDOM WALKS." Journal of the Institute of Mathematics of Jussieu 14, no. 3 (May 8, 2014): 451–91. http://dx.doi.org/10.1017/s1474748014000073.

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We study the spectral theory of a reversible Markov chain This random walk depends on a parameter $h\in ]0,h_{0}]$ which is roughly the size of each step of the walk. We prove uniform bounds with respect to $h$ on the rate of convergence to equilibrium, and the convergence when $h\rightarrow 0$ to the associated hypoelliptic diffusion.
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22

Mijatović, Aleksandar. "Spectral properties of trinomial trees." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 463, no. 2083 (April 10, 2007): 1681–96. http://dx.doi.org/10.1098/rspa.2007.1845.

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In this paper, we prove that the probability kernel of a random walk on a trinomial tree converges to the density of a Brownian motion with drift at the rate O ( h 4 ), where h is the distance between the nodes of the tree. We also show that this convergence estimate is optimal in which the density of the random walk cannot converge at a faster rate. The proof is based on an application of spectral theory to the transition density of the random walk. This yields an integral representation of the discrete probability kernel that allows us to determine the convergence rate.
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23

RINGHOFER, CHRISTIAN. "ON THE CONVERGENCE OF SPECTRAL METHODS FOR THE WIGNER-POISSON PROBLEM." Mathematical Models and Methods in Applied Sciences 02, no. 01 (March 1992): 91–111. http://dx.doi.org/10.1142/s0218202592000077.

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We analyze the convergence properties of a spectral collocation method for the Wigner-Poisson equation, a nonlinear pseudodifferential equation describing quantum mechanical transport phenomena. Spectral accuracy and nonlinear stability of the momentum discretization are proven. The convergence results are verified numerically on a test sample.
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24

Ghanbari, Mahdi, Tahir Ahmad, Norma Alias, and Mohammadreza Askaripour. "Global convergence of two spectral conjugate gradient methods." ScienceAsia 39, no. 3 (2013): 306. http://dx.doi.org/10.2306/scienceasia1513-1874.2013.39.306.

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25

Causley, Mathew, and David Seal. "On the convergence of spectral deferred correction methods." Communications in Applied Mathematics and Computational Science 14, no. 1 (February 9, 2019): 33–64. http://dx.doi.org/10.2140/camcos.2019.14.33.

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26

Ambrosio, Luigi, and Shouhei Honda. "Local spectral convergence in RCD∗(K,N) spaces." Nonlinear Analysis 177 (December 2018): 1–23. http://dx.doi.org/10.1016/j.na.2017.04.003.

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27

Mikosch, T., and R. Norvaiša. "Uniform convergence of the empirical spectral distribution function." Stochastic Processes and their Applications 70, no. 1 (October 1997): 85–114. http://dx.doi.org/10.1016/s0304-4149(97)00053-7.

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28

Tadmor, Eitan. "Convergence of Spectral Methods for Nonlinear Conservation Laws." SIAM Journal on Numerical Analysis 26, no. 1 (February 1989): 30–44. http://dx.doi.org/10.1137/0726003.

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29

Meaney, Christopher, Detlef Müller, and Elena Prestini. "A.e. convergence of spectral sums on Lie groups." Annales de l’institut Fourier 57, no. 5 (2007): 1509–20. http://dx.doi.org/10.5802/aif.2303.

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30

Kooperberg, Charles, Charles J. Stone, and Young K. Truong. "RATE OF CONVERGENCE FOR LOGSPLINE SPECTRAL DENSITY ESTIMATION." Journal of Time Series Analysis 16, no. 4 (July 1995): 389–401. http://dx.doi.org/10.1111/j.1467-9892.1995.tb00241.x.

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31

Huang, Jingfang, Jun Jia, and Michael Minion. "Accelerating the convergence of spectral deferred correction methods." Journal of Computational Physics 214, no. 2 (May 2006): 633–56. http://dx.doi.org/10.1016/j.jcp.2005.10.004.

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32

Wang, Changyu, Qian Liu, and Xinmin Yang. "Convergence properties of nonmonotone spectral projected gradient methods." Journal of Computational and Applied Mathematics 182, no. 1 (October 2005): 51–66. http://dx.doi.org/10.1016/j.cam.2004.10.018.

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33

Anné, Colette, and Olaf Post. "Wildly perturbed manifolds: norm resolvent and spectral convergence." Journal of Spectral Theory 11, no. 1 (March 1, 2021): 229–79. http://dx.doi.org/10.4171/jst/340.

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34

Xie, Junshan. "Second-Order Moment Convergence Rates for Spectral Statistics of Random Matrices." Abstract and Applied Analysis 2013 (2013): 1–7. http://dx.doi.org/10.1155/2013/595912.

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This paper considers the precise asymptotics of the spectral statistics of random matrices. Following the ideas of Gut and Spătaru (2000) and Liu and Lin (2006) on the precise asymptotics of i.i.d. random variables in the context of the complete convergence and the second-order moment convergence, respectively, we will establish the precise second-order moment convergence rates of a type of series constructed by the spectral statistics of Wigner matrices or sample covariance matrices.
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35

Kay, S., and L. Pakula. "Convergence of the Multidimensional Minimum Variance Spectral Estimator for Continuous and Mixed Spectra." IEEE Signal Processing Letters 17, no. 1 (January 2010): 28–31. http://dx.doi.org/10.1109/lsp.2009.2031715.

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36

Litvinova, Man Nen, Victor Krishtop, Evgeniy Tolstov, Vladimir Troilin, Larisa Alekseeva, and Veronika Litvinova. "Upconversion of Broadband Infrared Radiation into Visible Light for Different Pumping Parameters." Journal of Spectroscopy 2013 (2013): 1–5. http://dx.doi.org/10.1155/2013/631510.

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The influence of pump radiation parameters such as the polarization and the spectral width of infrared radiation on the conversion of broadband radiation in lithium niobate crystals was investigated. The spectra of converted radiation were calculated for two types of phase matching in the negative uniaxial crystal by taking into account the convergence of the light beam in the crystal. Experimental spectra were obtained and compared with the calculated spectra.
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37

Wills, M. D. "Extension of Spectral Scales to Unbounded Operators." International Journal of Mathematics and Mathematical Sciences 2010 (2010): 1–33. http://dx.doi.org/10.1155/2010/713563.

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We extend the notion of a spectral scale ton-tuples of unbounded operators affiliated with a finite von Neumann Algebra. We focus primarily on the single-variable case and show that many of the results from the bounded theory go through in the unbounded situation. We present the currently available material on the unbounded multivariable situation. Sufficient conditions for a set to be a spectral scale are established. The relationship between convergence of operators and the convergence of the corresponding spectral scales is investigated. We establish a connection between the Akemann et al. spectral scale (1999) and that of Petz (1985).
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38

Kulkarni, Rekha P., and N. Gnaneshwar. "Spectral refinement using a new projection method." ANZIAM Journal 46, no. 2 (October 2004): 203–24. http://dx.doi.org/10.1017/s1446181100013791.

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AbstractIn this paper we consider two spectral refinement schemes, elementary and double iteration, for the approximation of eigenelements of a compact operator using a new approximating operator. We show that the new method performs better than the Galerkin, projection and Sloan methods. We obtain precise orders of convergence for the approximation of eigenelements of an integral operator with a smooth kernel using either the orthogonal projection onto a spline space or the interpolatory projection at Gauss points onto a discontinuous piecewise polynomial space. We show that in the double iteration scheme the error for the eigenvalue iterates using the new method is of the order of , where h is the mesh of the partition and k = 0, 1, 2,… denotes the step of the iteration. This order of convergence is to be compared with the orders in the Galerkin and projection methods and in the Sloan method. The error in eigenvector iterates is shown to be of the order of in the new method, in the Galerkin and projection methods and in the Sloan method. Similar improvement is observed in the case of the elementary iteration. We show that these orders of convergence are preserved in the corresponding discrete methods obtained by replacing the integration by a numerical quadrature formula. We illustrate this improvement in the order of convergence by numerical examples.
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39

Faou, E., and V. Gradinaru. "Gauss-Hermite wave packet dynamics: convergence of the spectral and pseudo-spectral approximation." IMA Journal of Numerical Analysis 29, no. 4 (November 20, 2008): 1023–45. http://dx.doi.org/10.1093/imanum/drn041.

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40

Selmi, Ridha. "Convergence results for MHD system." International Journal of Mathematics and Mathematical Sciences 2006 (2006): 1–19. http://dx.doi.org/10.1155/ijmms/2006/28704.

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A magnetohydrodynamic system is investigated in both cases of the periodic domainT3and the whole spaceR3. Existence and uniqueness of strong solution are proved. Asymptotic behavior of the solution when the Rossby numberεgoes to zero is studied. The proofs use the spectral properties of the penalization operator and involve Friedrich's method, Schochet's methods, and product laws in Sobolev spaces of sufficiently large exponents.
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41

ELGART, ALEXANDER, and JEFFREY H. SCHENKER. "A STRONG OPERATOR TOPOLOGY ADIABATIC THEOREM." Reviews in Mathematical Physics 14, no. 06 (June 2002): 569–84. http://dx.doi.org/10.1142/s0129055x02001247.

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We prove an adiabatic theorem for the evolution of spectral data under a weak additive perturbation in the context of a system without an intrinsic time scale. For continuous functions of the unperturbed Hamiltonian the convergence is in norm while for a larger class functions, including the spectral projections associated to embedded eigenvalues, the convergence is in the strong operator topology.
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42

Jiang, Huabin, Songhai Deng, Xiaodong Zheng, and Zhong Wan. "Global Convergence of a Modified Spectral Conjugate Gradient Method." Journal of Applied Mathematics 2012 (2012): 1–13. http://dx.doi.org/10.1155/2012/641276.

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A modified spectral PRP conjugate gradient method is presented for solving unconstrained optimization problems. The constructed search direction is proved to be a sufficiently descent direction of the objective function. With an Armijo-type line search to determinate the step length, a new spectral PRP conjugate algorithm is developed. Under some mild conditions, the theory of global convergence is established. Numerical results demonstrate that this algorithm is promising, particularly, compared with the existing similar ones.
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43

Wang, Yuyu, and Jianbo Wang. "The Convergence of Some Products in the Adams Spectral Sequence." MATHEMATICA SCANDINAVICA 117, no. 2 (December 14, 2015): 304. http://dx.doi.org/10.7146/math.scand.a-22871.

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In this paper, we will use the family of homotopy elements $\zeta_n\in\pi_*S$, represented by $h_0b_n\in \operatorname{Ext}_A^{3,p^{n+1} q+q}(\mathsf{Z}_p, \mathsf{Z}_p)$ in the Adams spectral sequence, to detect a $\zeta_n$-related family $\gamma_{s+3}\beta_2\zeta_{n-1}$ in $\pi_*S$. Our main methods are the Adams spectral sequence and the May spectral sequence, here prime $p\geq 7$, $n>3$, $q=2(p-1)$.
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44

Omran, A. K., M. A. Zaky, A. S. Hendy, and V. G. Pimenov. "An Efficient Hybrid Numerical Scheme for Nonlinear Multiterm Caputo Time and Riesz Space Fractional-Order Diffusion Equations with Delay." Journal of Function Spaces 2021 (December 6, 2021): 1–13. http://dx.doi.org/10.1155/2021/5922853.

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In this paper, we construct and analyze a linearized finite difference/Galerkin–Legendre spectral scheme for the nonlinear multiterm Caputo time fractional-order reaction-diffusion equation with time delay and Riesz space fractional derivatives. The temporal fractional orders in the considered model are taken as 0 < β 0 < β 1 < β 2 < ⋯ < β m < 1 . The problem is first approximated by the L 1 difference method on the temporal direction, and then, the Galerkin–Legendre spectral method is applied on the spatial discretization. Armed by an appropriate form of discrete fractional Grönwall inequalities, the stability and convergence of the fully discrete scheme are investigated by discrete energy estimates. We show that the proposed method is stable and has a convergent order of 2 − β m in time and an exponential rate of convergence in space. We finally provide some numerical experiments to show the efficacy of the theoretical results.
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45

Peligrad, Costel, and Magda Peligrad. "The limiting spectral distribution in terms of spectral density." Random Matrices: Theory and Applications 05, no. 01 (January 2016): 1650003. http://dx.doi.org/10.1142/s2010326316500039.

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For a large class of symmetric random matrices with correlated entries, selected from stationary random fields of centered and square integrable variables, we show that the limiting distribution of eigenvalue counting measure always exists and we describe it via an equation satisfied by its Stieltjes transform. No rate of convergence to zero of correlations is imposed, therefore the process is allowed to have long memory. In particular, if the symmetrized matrices are constructed from stationary Gaussian random fields which have spectral density, the result of this paper gives a complete solution to the limiting eigenvalue distribution. More generally, for matrices whose entries are functions of independent and identically distributed random variables the result also holds.
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46

Li, Cui-Xia, and Su-Hua Li. "Comparison Theorems of Spectral Radius for Splittings of Matrices." Journal of Applied Mathematics 2014 (2014): 1–5. http://dx.doi.org/10.1155/2014/573024.

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A class of the iteration method from the double splitting of coefficient matrix for solving the linear system is further investigated. By structuring a new matrix, the iteration matrix of the corresponding double splitting iteration method is presented. On the basis of convergence and comparison theorems for single splittings, we present some new convergence and comparison theorems on spectral radius for splittings of matrices.
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47

Curti, M., J. W. Jansen, and E. A. Lomonova. "Convergence analysis of spectral element method for magnetic devices." International Journal of Applied Electromagnetics and Mechanics 57 (April 8, 2018): 43–49. http://dx.doi.org/10.3233/jae-182297.

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48

Rubio, Francisco, and Xavier Mestre. "Spectral convergence for a general class of random matrices." Statistics & Probability Letters 81, no. 5 (May 2011): 592–602. http://dx.doi.org/10.1016/j.spl.2011.01.004.

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49

Cicone, Antonio, Carlo Garoni, and Stefano Serra-Capizzano. "Spectral and convergence analysis of the Discrete ALIF method." Linear Algebra and its Applications 580 (November 2019): 62–95. http://dx.doi.org/10.1016/j.laa.2019.06.021.

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50

Du, Xianglin, and Jinkui Liu. "Global Convergence Of A Spectral Hs Conjugate Gradient Method." Procedia Engineering 15 (2011): 1487–92. http://dx.doi.org/10.1016/j.proeng.2011.08.276.

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