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Toeplitz matrix
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==References== {{refbegin}} *{{citation | last1 = Bojanczyk | first1 = A. W. | last2 = Brent | first2 = R. P. | last3 = de Hoog | first3 = F. R. | last4 = Sweet | first4 = D. R. | year = 1995 | title = On the stability of the Bareiss and related Toeplitz factorization algorithms | journal = [[SIAM Journal on Matrix Analysis and Applications]] | volume = 16 | pages = 40–57 | doi = 10.1137/S0895479891221563| arxiv = 1004.5510 | s2cid = 367586 }} *{{citation|first1=Albrecht| last1= Böttcher| first2=Sergei M. | last2= Grudsky|title=Toeplitz Matrices, Asymptotic Linear Algebra, and Functional Analysis|url=https://books.google.com/books?id=Dmr0BwAAQBAJ&pg=PA1|year=2012|publisher=Birkhäuser|isbn=978-3-0348-8395-5}} *{{citation | first= R. P. | last= Brent | author-link=Richard P. Brent | year= 1999 | contribution= Stability of fast algorithms for structured linear systems| title= Fast Reliable Algorithms for Matrices with Structure | editor1-first= T. | editor1-last= Kailath | editor2-first= A. H. | editor2-last=Sayed | publisher= [[Society for Industrial and Applied Mathematics|SIAM]] | pages=103–116|doi=10.1137/1.9781611971354.ch4| hdl= 1885/40746 | s2cid= 13905858 | hdl-access= free }} *{{citation|last1=Chan |first1=R. H.-F.| last2= Jin| first2= X.-Q. | year=2007 | title= An Introduction to Iterative Toeplitz Solvers | publisher= [[Society for Industrial and Applied Mathematics|SIAM]]|doi=10.1137/1.9780898718850|isbn=978-0-89871-636-8 }} *{{citation | last1 = Chandrasekeran | first1 = S. | last2 = Gu | first2 = M. | last3 = Sun | first3 = X. | last4 = Xia | first4 = J. | last5 = Zhu | first5 = J. | year = 2007 | title = A superfast algorithm for Toeplitz systems of linear equations | journal = [[SIAM Journal on Matrix Analysis and Applications]] | volume = 29 | issue = 4| pages = 1247–66 | doi = 10.1137/040617200| citeseerx = 10.1.1.116.3297 }} *{{citation | last1 = Chen | first1 = W. W. | last2 = Hurvich | first2 = C. M. | last3 = Lu | first3 = Y. | year = 2006 | title = On the correlation matrix of the discrete Fourier transform and the fast solution of large Toeplitz systems for long-memory time series | journal = [[Journal of the American Statistical Association]] | volume = 101 | issue = 474| pages = 812–822 | doi = 10.1198/016214505000001069| citeseerx = 10.1.1.574.4394 | s2cid = 55893963 }} *{{citation | last=Hayes | first=Monson H.|title= Statistical digital signal processing and modeling | year = 1996 | publisher = Wiley | isbn = 0-471-59431-8}} *{{citation | last1 = Krishna | first1 = H. | last2=Wang | first2= Y. | title = The Split Levinson Algorithm is weakly stable | journal = [[SIAM Journal on Numerical Analysis]] | volume = 30 | issue = 5 | pages = 1498–1508 | year = 1993 | url = http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=SJNAAM000030000005001498000001&idtype=cvips&gifs=yes | doi = 10.1137/0730078| url-access = subscription }} *{{citation| last=Monahan | first= J. F. | year=2011 | title=Numerical Methods of Statistics | publisher= [[Cambridge University Press]] |isbn=978-1-139-08211-2 |doi=10.1017/CBO9780511977176}} *{{citation| last1=Mukherjee | first1= Bishwa Nath | first2= Sadhan Samar | last2= Maiti | year= 1988 | title=On some properties of positive definite Toeplitz matrices and their possible applications | journal= [[Linear Algebra and Its Applications]] | volume= 102 | pages= 211–240 | doi= 10.1016/0024-3795(88)90326-6 | url= https://core.ac.uk/download/pdf/82070573.pdf| doi-access= free }} *{{citation|last1=Press | first1=W. H. | last2= Teukolsky | first2= S. A. | last3= Vetterling | first3= W. T. | last4= Flannery | first4= B. P. | year=2007 | title= Numerical Recipes: The Art of Scientific Computing | edition= 3rd | publisher= [[Cambridge University Press]] | isbn= 978-0-521-88068-8| title-link=Numerical Recipes }} *{{citation | last = Stewart | first = M. | year = 2003 | title = A superfast Toeplitz solver with improved numerical stability | journal = [[SIAM Journal on Matrix Analysis and Applications]] | volume = 25 | issue = 3| pages = 669–693 | doi = 10.1137/S089547980241791X | s2cid = 15717371 }} *{{citation | last1 = Yang | first1 = Zai | last2 = Xie | first2 = Lihua | last3 = Stoica | first3 = Petre | year = 2016 | title = Vandermonde decomposition of multilevel Toeplitz matrices with application to multidimensional super-resolution | journal = [[IEEE Transactions on Information Theory]] | volume = 62 | issue = 6 | pages = 3685–3701 | doi = 10.1109/TIT.2016.2553041 | arxiv = 1505.02510 | s2cid = 6291005 }} {{refend}}
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