Toeplitz Matrices, Asymptotic Linear Algebra, and Functional Analysis by Albrecht BöttcherToeplitz Matrices, Asymptotic Linear Algebra, and Functional Analysis by Albrecht Böttcher

Toeplitz Matrices, Asymptotic Linear Algebra, and Functional Analysis

byAlbrecht Böttcher, Sergei M. Grudsky

Paperback | November 5, 2012

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The subject of this text is the relation between the properties of infinite Toeplitz matrices ao a_I a_2 al ao a_I a2 al ao and their large finite sections This is very big and even inexhaustible subject, and therefore we must limit ourselves to a few concrete problems here. We will focus our attention on singular values. The singular values of An are the eigenvalues of (A<_an29_i2f_2.20_the20_properties20_of20_the20_singular20_values20_of20_an20_for20_fixed20_n20_28_or2c_20_as20_in20_so-called20_interlacing20_theorems2c_20_for20_some20_consecutive20_n29_20_are20_studied20_in20_linear20_algebra.20_the20_problem20_of20_determining20_the20_singular20_values20_of20_an20_for20_large20_n20_28_say20_n20_3d_20_70029_20_is20_a20_business20_of20_numerical20_linear20_algebra.20_the20_behavior20_of20_the20_singular20_2320_values20_of20_an20_for20_n20_--2b_20_0020_28_or2c_20_say2c_20_for20_n20_3d_20_1020_29_20_is20_a20_concern20_of20_asymptotic20_linear20_algebra.20_finally2c_20_the20_investigation20_of20_the20_properties20_of20_the20_infinite20_matrix20_a20_is20_a20_task20_of20_functional20_analysis.20_to20_get20_an20_idea20_of20_what20_this20_text20_is20_about2c_20_we20_cite20_a20_few20_questions20_we20_will20_consider.20_preface20_viii20_question20_1.20_does20_the20_smallest20_singular20_value20_8120_28_an29_20_stay20_away20_from20_zero20_as20_n20_-t20_oo3f_20_because20_this20_is20_the20_question20_whether20_the20_norms20_iia3b_3b_11120_are20_uniformly20_bounded20_for20_all20_sufficiently20_large20_n. .="" the="" properties="" of="" singular="" values="" an="" for="" fixed="" n="" _28_or2c_="" as="" in="" so-called="" interlacing="" _theorems2c_="" some="" consecutive="" _n29_="" are="" studied="" linear="" algebra.="" problem="" determining="" large="" _28_say="" is="" a="" business="" numerical="" behavior="" 23="" _--2b_="" 00="" _say2c_="" _29_="" concern="" asymptotic="" _finally2c_="" investigation="" infinite="" matrix="" task="" functional="" analysis.="" to="" get="" idea="" what="" this="" text="" _about2c_="" we="" cite="" few="" questions="" will="" consider.="" preface="" viii="" question="" 1.="" does="" smallest="" value="" 81="" _28_an29_="" stay="" away="" from="" zero="" -t="" _oo3f_="" because="" whether="" norms="" _iia3b_3b_111="" uniformly="" bounded="" all="" sufficiently="">
Title:Toeplitz Matrices, Asymptotic Linear Algebra, and Functional AnalysisFormat:PaperbackDimensions:112 pagesPublished:November 5, 2012Publisher:Springer-Verlag/Sci-Tech/TradeLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:3034895488

ISBN - 13:9783034895484

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Table of Contents

1 Infinite Toeplitz Matrices.- 2 C*-Algebras in Action.- 3 Instability.- 4 Condition Numbers.- 5 Singular Values.- Notation Index.