References

1

N. I. Akhiezer. The Classical Moment Problem and Some Related Questions in Analysis. Hafner, New York, 1965.

2

G. S. Ammar and P. Gader. New decompositions of the inverse of a Toeplitz matrix. In M. A. Kaashoek, J. H. van Schuppen, and A. C. N. Ran, editors, Signal Processing, Scattering and Operator Theory, and Numerical Methods, pages 421--428. Birkhäuser, 1990.

3

G. S. Ammar and P. Gader. A variant of the Gohberg--Semencul formula involving circulant matrices. SIAM J. Matrix Anal. Appl., 12:534--540, 1991.

4

G. S. Ammar and W. B. Gragg. Implementation and use of the generalized Schur algorithm. In C. I. Byrnes and A. Lindquist, editors, Computational and Combinatorial Methods in Systems Theory, pages 265--280. North-Holland, Amsterdam, 1986.

5

G. S. Ammar and W. B. Gragg. The generalized Schur algorithm for the superfast solution of Toeplitz systems. In J. Gilewicz, M. Pindor, and W. Siemaszko, editors, Rational Approximation and its Applications in Mathematics and Physics, number 1237 in Lecture Notes in Mathematics, pages 315--330. Springer-Verlag, Berlin, 1987.

6

G. S. Ammar and W. B. Gragg. Superfast solution of real positive definite Toeplitz systems. SIAM J. Matrix Anal. Appl., 9:61--76, 1988.

7

G. S. Ammar and W. B. Gragg. Numerical experience with a superfast real Toeplitz solver. Linear Algebra and its Applications, 121:185--206, 1989.

8

E. H. Bareiss. Numerical solution of linear equations with Toeplitz and vector Toeplitz matrices. Numer. Math., 13:404--424, 1969.

9

R. R. Bitmead and B. D. O. Anderson. Asymptotically fast solution of Toeplitz and related systems of linear equations. Lin. Alg. Appl., 34:103--116, 1980.

10

R. E. Blahut. Fast Algorithms for Digital Signal Processing. Addison-Wesley, Reading, MA, 1985.

11

A. W. Bojanczyk, R. P. Brent, F. R. D. Hoog, and D. R. Sweet. On the stability of the Bareiss and related Toeplitz factorization algorithms. SIAM J. Matrix Anal. Appl., 16:40--57, 1995.

12

E. Bozzo. Algebras of higher dimension for displacement decompositions and computations with Toeplitz plus Hankel matrices. Lin. Alg. Appl., 230:127--150, 1995.

13

E. Bozzo and C. Di Fiore. On the use of certain matrix algebras associated with real discrete transforms in matrix displacement decomposition. SIAM J. Matrix Anal. Appl., 16:312--326, 1995.

14

R. P. Brent, F. G. Gustavson, and D. Y. Y. Yun. Fast solution of Toeplitz systems of equations and computation of Padé approximants. J. Algorithms, 1:259--295, 1980.

15

F. de Hoog. A new algorithm for solving Toeplitz systems of equations. Lin. Alg. Appl., 88/89:123--138, 1987.

16

C. Di Fiore and P. Zellini. Matrix decompositions using displacement rank and classes of commutative matrix algebras. Lin. Alg. Appl., 229:49--100, 1995.

17

J. Durbin. The fitting of time-series models. Rev. Int. Inst. Statist., 28:233--243, 1960.

18

B. Friedlander, M. Morf, T. Kailath, and L. Ljung. New inversion formulas for matrices classified in terms of their distance from Toeplitz matrices. Lin. Alg. Appl., 27:31--60, 1979.

19

P. Gader. Displacement operator based decompositions of matrices using circulants or other group matrices. Lin. Alg. Appl., 139:111--131, 1990.

20

I. Gohberg, T. Kailath, I. Koltracht, and P. Lancaster. Linear complexity parallel algorithms for linear systems of equations with recursive structure. Lin. Alg. Appl., 88/89:271--315, 1987.

21

I. Gohberg, I. Koltracht, and D. Xiao. Condition and accuracy of algorithms for computing Schur coefficients of Toeplitz matrices. SIAM J. Matrix Anal. Appl., 15:1290--1309, 1994.

22

I. Gohberg and V. Olshevsky. Complexity of multiplication with vectors for structured matrices. Lin. Alg. Appl., 202:163--192, 1994.

23

I. C. Gohberg and I. A. Feldman. Convolution Equations and Projection Methods for Their Solution. American Math. Soc., Providence, RI, 1974.

24

G. H. Golub and C. F. Van Loan. Matrix Computations. Johns Hopkins University Press, second edition, 1989.

25

U. Grenander and G. Szego. Toeplitz Forms and Their Applications. Chelsea, New York, second edition, 1984.

26

G. Heinig and K. Rost. Algebraic Methods for Toeplitz-like Matrices and Operators. Akademie-Verlag, Berlin, 1984.

27

J. R. Jain. An efficient algorithm for a large Toeplitz set of linear equations. IEEE Trans. Acoust., Speech, Signal Proc., 27:612--615, 1979.

28

T. Kailath. A theorem of I. Schur and its impact on modern signal processing. In I. Gohberg, editor, I. Schur Methods in Operator Theory and Signal Processing, pages 9--30. Birkhäuser Verlag, Boston, 1986.

29

T. Kailath and J. Chun. Generalized displacement structure for block-Toeplitz, Toeplitz-block, and Toeplitz-derived matrices. SIAM J. Matrix Anal. Appl., 15(1):114--128, 1994.

30

T. Kailath, S.-Y. Kung, and M. Morf. Displacement ranks of matrices and linear equations. J. Math. Anal. and Appl., 68:395--407, 1979.

31

T. Kailath and A. H. Sayed. Displacement structure: Theory and applications. SIAM Review, 37:297--386, 1995.

32

T. Kailath, A. Vieira, and M. Morf. Inverses of Toeplitz operators, innovations, and orthogonal polynomials. SIAM Rev., 20:106--119, 1978.

33

N. Levinson. The Wiener RMS (root-mean-square) error criterion in filter design and prediction. J. Math. Phys., 25:261--278, 1947.

34

B. R. Musicus. Levinson and fast Cholesky algorithms for Toeplitz and almost Toeplitz matrices. Technical report, Research Lab. of Electronics, M. I. T., 1984.

35

I. Schur. Uber potenzreihen, die in Innern des Einheitskrises Beschränkt Sind. J. Reine Angew. Math., 147:205--232, 1917. English translation in: I. Schur Methods in Operator Theory and Signal Processing, I. Gohberg, ed., Birkhäuser, 1986, 31--89.

36

G. Szego. Orthogonal Polynomials. American Math. Soc., Providence, 1939.

37

W. F. Trench. An algorithm for the inversion of finite Toeplitz matrices. J. Soc. Indust. Appl. Math., 12:515--522, 1964.