Editing Levinson recursion (section)

== References ==
'''Defining sources'''
* Levinson, N. (1947). "The Wiener RMS error criterion in filter design and prediction." ''J. Math. Phys.'', v. 25, pp.&nbsp;261–278.
* Durbin, J. (1960). "The fitting of time series models." ''Rev. Inst. Int. Stat.'', v. 28, pp.&nbsp;233–243.
* Trench, W. F. (1964).  "An algorithm for the inversion of finite Toeplitz matrices."  ''J. Soc. Indust. Appl. Math.'', v. 12, pp.&nbsp;515–522.
* Musicus, B. R. (1988). "Levinson and Fast Choleski Algorithms for Toeplitz and Almost Toeplitz Matrices." ''RLE TR'' No. 538, MIT. [http://dspace.mit.edu/bitstream/1721.1/4954/1/RLE-TR-538-20174000.pdf]
* Delsarte, P. and Genin, Y. V. (1986). "The split Levinson algorithm." ''IEEE Transactions on Acoustics, Speech, and Signal Processing'', v. ASSP-34(3), pp.&nbsp;470–478.
'''Further work'''
*{{cite journal | 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 }}
*[[Richard P. Brent|Brent R.P.]] (1999), "Stability of fast algorithms for structured linear systems", ''Fast Reliable Algorithms for Matrices with Structure'' (editors—T. Kailath, A.H. Sayed), ch.4 ([[Society for Industrial and Applied Mathematics|SIAM]]).
* Bunch, J. R. (1985). "Stability of methods for solving Toeplitz systems of equations." ''SIAM J. Sci. Stat. Comput.'', v. 6, pp.&nbsp;349–364. [https://doi.org/10.1137/0906025]
*{{cite journal | last = Krishna | first = H. |author2=Wang, Y.  | title = The Split Levinson Algorithm is weakly stable | journal = [[SIAM Journal on Numerical Analysis]] | volume = 30 | issue = 5 | pages = 1498–1508 | date = 1993 | url = http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=SJNAAM000030000005001498000001&idtype=cvips&gifs=yes | doi = 10.1137/0730078| url-access = subscription }}
'''Summaries'''
* Bäckström, T. (2004). "2.2. Levinson–Durbin Recursion." ''Linear Predictive Modelling of Speech – Constraints and Line Spectrum Pair Decomposition.'' Doctoral thesis. Report no. 71 / Helsinki University of Technology, Laboratory of Acoustics and Audio Signal Processing. Espoo, Finland. [http://lib.tkk.fi/Diss/2004/isbn9512269473/isbn9512269473.pdf]
* Claerbout, Jon F. (1976). "Chapter 7 – Waveform Applications of Least-Squares." ''Fundamentals of Geophysical Data Processing.''  Palo Alto: Blackwell Scientific Publications. [https://web.archive.org/web/20060921204908/http://sep.stanford.edu/oldreports/fgdp2/fgdp_07.pdf]
*{{Citation |last1=Press|first1=WH|last2=Teukolsky|first2=SA|last3=Vetterling|first3=WT|last4=Flannery|first4=BP|year=2007|title=Numerical Recipes: The Art of Scientific Computing|edition=3rd|publisher=Cambridge University Press| publication-place=New York|isbn=978-0-521-88068-8|chapter=Section 2.8.2. Toeplitz Matrices|chapter-url=http://apps.nrbook.com/empanel/index.html?pg=96}}
* Golub, G.H., and Loan, C.F. Van (1996). "Section 4.7 : Toeplitz and related Systems" ''Matrix Computations'', Johns Hopkins University Press

[[Category:Matrices (mathematics)]]
[[Category:Numerical analysis]]