Access the full text.
Sign up today, get DeepDyve free for 14 days.
Loading next page...
/lp/springer-journals/the-schur-algorithm-and-its-applications-EtHzfRbLMM
References (57)
-
J. Makhoul (1977)
Stable and efficient lattice methods for linear predictionIEEE Transactions on Acoustics, Speech, and Signal Processing, 25
-
(1967)
Properties of the S-Matrix of the One-Dimensional Schrodinger Equation -
A. Bultheel (1979)
Towards an error analysis of fast Toeplitz factorization -
J. Rissanen (1973)
Algorithms for triangular decomposition of block Hankel and Toeplitz matrices with application to factoring positive matrix polynomialsMathematics of Computation, 27
-
B. Musicus (1981)
Technical Report -
(1982)
Stochastic Modeling with Orthogonal Filters -
B. Friedlander (1982)
Lattice methods for spectral estimationProceedings of the IEEE, 70
-
S. Hoffman, N. Akhiezer (1968)
The Classical Moment Problem.American Mathematical Monthly, 75
-
P. Dewilde, A. Vieira, T. Kailath (1978)
On a generalized Szegö- Levinson realization algorithm for optimal linear predictors based on a network synthesis approachIEEE Transactions on Circuits and Systems, 25
-
R. Bellman, G. Wing, E. Denman (1977)
An introduction to invariant imbeddingProceedings of the IEEE, 65
-
(1978)
Three-Chip System Synthesizes Human Speech -
Irvin Kay, Harry Moses (1982)
Inverse scattering papers, 1955-1962 -
T. Kailath, B. Levy, L. Ljung, M. Morf (1979)
The Factorization and Representation of Operators in the Algebra Generated by Toeplitz OperatorsSiam Journal on Applied Mathematics, 37
-
V. Zakharov, A. Shabat (1970)
Exact Theory of Two-dimensional Self-focusing and One-dimensional Self-modulation of Waves in Nonlinear MediaJournal of Experimental and Theoretical Physics, 34
-
P. Dewilde, J. Fokkema, I. Widya (1981)
Inverse Scattering and Linear Prediction, the Time Continuous Case -
K. Bube, R. Burridge (1983)
The One-Dimensional Inverse Problem of Reflection SeismologySiam Review, 25
-
A. Yagle, B. Levy (1984)
Application of the Schur algorithm to the inverse problem for a layered acoustic mediumJournal of the Acoustical Society of America, 76
-
Herrn Schur
Über Potenzreihen, die im Innern des Einheitskreises beschränkt sind.Journal für die reine und angewandte Mathematik (Crelles Journal), 1918
-
W. W. Symes (1981)
Stable Solution of the Inverse Reflection Problem for a Smoothly Stratified Elastic MediumSIAM J. Math. Anal., 12
-
T. Crystal (1977)
Linear prediction of speechProceedings of the IEEE, 66
-
T. Kailath, A. Vieira, M. Morf (1975)
Inverses of Toeplitz operators, innovations, and orthogonal polynomials1975 IEEE Conference on Decision and Control including the 14th Symposium on Adaptive Processes
-
P. Dewilde, H. Dym (1981)
Schur recursions, error formulas, and convergence of rational estimators for stationary stochastic sequencesIEEE Trans. Inf. Theory, 27
-
E. Satorius, S. Alexander (1979)
Channel Equalization Using Adaptive Lattice AlgorithmsIEEE Trans. Commun., 27
-
J. Kraus, K. Carver (1973)
Electromagnetics -
W. Symes (1979)
The Inverse Reflection Problem for a Smoothly Stratified Elastic Medium. -
A. Bruckstein, B. Levy, T. Kailath (1985)
Differential methods in inverse scatteringSiam Journal on Applied Mathematics, 45
-
G. Kishi, M. Mitani, K. Kamata, S. Tsujii (1977)
A new realization scheme of digital filters--Row-wise addition configurationIEEE Transactions on Acoustics, Speech, and Signal Processing, 25
-
B. Gjevik, A. Nilsen, J. Höyen (1976)
AN ATTEMPT AT THE INVERSION OF REFLECTION DATAGeophysical Prospecting, 24
-
G. Lamb (1980)
Elements of soliton theory -
E. Deprettere, P. Dewilde (1980)
Orthogonal cascade realization of real multiport digital filtersInternational Journal of Circuit Theory and Applications, 8
-
E. Robinson (1982)
Spectral approach to geophysical inversion by Lorentz, Fourier, and Radon transformsProceedings of the IEEE, 70
-
J. Ware, K. Aki (1969)
Continuous and Discrete Inverse‐Scattering Problems in a Stratified Elastic Medium. I. Plane Waves at Normal IncidenceJournal of the Acoustical Society of America, 45
-
M. Morf (1974)
Fast Algorithms for Multivariable Systems -
B. Gopinath, M. Sondhi (1971)
Inversion of the telegraph equation and the synthesis of nonuniform lines, 59
-
A. M. Bruckstein, B. C. Levy, T. Kailath (1983)
Technical Report LIDS-P-1313 -
T. Kailath, A. Vieira, M. Morf (1978)
Inverses of Toeplitz Operators, Innovations, and Orthogonal PolynomialsSIAM Rev., 20
-
M. Howard (1983)
Inverse scattering for a layered acoustic medium using the first‐order equations of motionGeophysics, 48
-
P. Deift, E. Trubowitz (1979)
Inverse scattering on the lineCommunications on Pure and Applied Mathematics, 32
-
R. Redheffer (1962)
On the Relation of Transmission-Line Theory to Scattering and Transfer†Journal of Mathematics and Physics, 41
-
K. P. Bube, R. Burridge (1983)
The One-Dimensional Problem of Reflection SeismologySIAM Rev., 25
-
T. Hida (1983)
Stochastic systems: The mathematics of filtering and identification and applicationsActa Applicandae Mathematica, 1
-
R. Carroll, F. Santosa, L. Paynec (1981)
Scattering techniques for a one dimensional inverse problem in geophysicsMathematical Methods in The Applied Sciences, 3
-
M. J. Ablowitz, H. Segur (1981)
Solitons and the Inverse Scattering Transform -
T. Clarke (1984)
Full reconstruction of a layered elastic medium from P-SV slant-stack dataGeophysical Journal International, 78
-
M. Jaulent (1982)
The inverse scattering problem for LCRG transmission linesJournal of Mathematical Physics, 23
-
J. Berryman, R. Greene (1980)
Discrete inverse methods for elastic waves in layered mediaGeophysics, 45
-
V. E. Zakharov, P. B. Shabat (1972)
Exact Theory of Two-Dimensional Self-Focusing and One-Dimensional Self-Modulation of Waves in Nonlinear MediaSoviet. Phys. JETP, 34
-
P. Delsarte, Y. Genin, Y. Kamp (1981)
On the role of the Nevanlinna–Pick problem in circuit and system theory†International Journal of Circuit Theory and Applications, 9
-
P. Dewilde (1982)
Mathematical Tools and Models for Control Systems Analysis and Signal Processing -
S. Coen (1981)
Density and compressibility profiles of a layered acoustic medium from precritical incidence dataGeophysics, 46
-
R. Newton (1981)
Inversion of reflection data for layered media: a review of exact methodsGeophysical Journal International, 65
-
A. Yagle, B. Levy (1985)
A layer-stripping solution of the inverse problem for a one-dimensional elastic mediumGeophysics, 50
-
S. Rao, T. Kailath (1984)
Orthogonal digital filters for VLSI implementation -
B. Gopinath, M. Sondhi (1970)
Determination of the shape of the human vocal tract from acoustical measurementsBell Syst. Tech. J., 49
-
M. Sondhi, J. Resnick (1983)
The inverse problem for the vocal tract: numerical methods, acoustical experiments, and speech synthesis.The Journal of the Acoustical Society of America, 73 3
-
F. Santosa, H. Schwetlick (1982)
INVERSION OF ACOUSTICAL IMPEDANCE PROFILE BY THE METHODS OF CHARACTERISTICS. -
K. Chadan, P. Sabatier (1977)
Inverse Problems in Quantum Scattering Theory
- Publisher
- Springer Journals
- Copyright
- Copyright
- Subject
- Mathematics; Computational Mathematics and Numerical Analysis; Applications of Mathematics; Partial Differential Equations; Probability Theory and Stochastic Processes; Calculus of Variations and Optimal Control; Optimization
- ISSN
- 0167-8019
- eISSN
- 1572-9036
- DOI
- 10.1007/BF00047331
- Publisher site
- See Article on Publisher Site
Abstract
The Schur algorithm and its time-domain counterpart, the fast Cholseky recursions, are some efficient signal processing algorithms which are well adapted to the study of inverse scattering problems. These algorithms use a layer stripping approach to reconstruct a lossless scattering medium described by symmetric two-component wave equations which model the interaction of right and left propagating waves. In this paper, the Schur and fast Chokesky recursions are presented and are used to study several inverse problems such as the reconstruction of nonuniform lossless transmission lines, the inverse problem for a layered acoustic medium, and the linear least-squares estimation of stationary stochastic processes. The inverse scattering problem for asymmetric two-component wave equations corresponding to lossy media is also examined and solved by using two coupled sets of Schur recursions. This procedure is then applied to the inverse problem for lossy transmission lines.
Journal
Acta Applicandae Mathematicae – Springer Journals
Published: May 3, 2004