메뉴 건너뛰기




Volumn 78, Issue 8, 1990, Pages 1327-1343

Tracking a Few Extreme Singular Values and Vectors in Signal Processing

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER SIMULATION; MATHEMATICAL TECHNIQUES--EIGENVALUES AND EIGENFUNCTIONS;

EID: 0025474239     PISSN: 00189219     EISSN: 15582256     Source Type: Journal    
DOI: 10.1109/5.58320     Document Type: Article
Times cited : (401)

References (70)
  • 3
    • 0019533482 scopus 로고
    • Principle component analysis in linear systems, controllability, observability, and Model Reduction
    • Feb.
    • B.C. Moore,"Principle component analysis in linear systems, controllability, observability, and Model Reduction," IEEE Trans on Automatic Control, vol TAC-26, no. 1, pp. 17-32, Feb. 1981.
    • (1981) IEEE Trans on Automatic Control , vol.TAC-26 , Issue.1 , pp. 17-32
    • Moore, B.C.1
  • 5
    • 0000750510 scopus 로고
    • On the generalized Karhunen-Loève expansion
    • Y.T. Chien and K. S. Fu, "On the generalized Karhunen-Loève expansion," IEEE Trans. Inform. Theory, vol. TI-13, no. 3, pp. 518-520, 1967.
    • (1967) IEEE Trans. Inform. Theory , vol.TI-13 , Issue.3 , pp. 518-520
    • Chien, Y.T.1    Fu, K.S.2
  • 6
    • 84948598093 scopus 로고
    • SVD algorithms for linear system approximation and spectrum estimation
    • JAI Press Inc.
    • S. Y. Kung and K. S. Arun, "SVD algorithms for linear system approximation and spectrum estimation," in Advances in Statistical Signal Processing, vol. 1, JAI Press Inc., 1987, pp. 203-250.
    • (1987) Advances in Statistical Signal Processing , vol.1 , pp. 203-250
    • Kung, S.Y.1    Arun, K.S.2
  • 7
    • 0003792312 scopus 로고
    • Englewood Cliffs, NJ: Prentice Hall
    • T. Kailath, Linear Systems. Englewood Cliffs, NJ: Prentice Hall, 1980.
    • (1980) Linear Systems
    • Kailath, T.1
  • 9
    • 84984498378 scopus 로고
    • Pure states, polarized waves and principal components in the spectra of multiple geophysical time series
    • J. C. Samson, "Pure states, polarized waves and principal components in the spectra of multiple geophysical time series," Geophys. Jour. Roy. Astr. Soc, vol. 72, no. 3, pp. 647-664, 1983.
    • (1983) Geophys. Jour. Roy. Astr. Soc , vol.72 , Issue.3 , pp. 647-664
    • Samson, J.C.1
  • 10
    • 33947542886 scopus 로고
    • Identification of electromagnetic sources
    • F. Glangeaud and C. Latombe, "Identification of electromagnetic sources," Annales Geophysicae, vol. 1, no. 3, pp. 245-252, 1983.
    • (1983) Annales Geophysicae , vol.1 , Issue.3 , pp. 245-252
    • Glangeaud, F.1    Latombe, C.2
  • 11
    • 84984520202 scopus 로고
    • The retrieval of harmonics from a covariance function
    • V. F. Pisarenko, "The retrieval of harmonics from a covariance function," Geophys. Jour. Roy. Astr. Soc, vol. 33, pp. 347-366, 1973.
    • (1973) Geophys. Jour. Roy. Astr. Soc , vol.33 , pp. 347-366
    • Pisarenko, V.F.1
  • 14
    • 0020833661 scopus 로고
    • Optimality of high-resolution array processing using the eigensystem approach
    • Oct.
    • G. Bienvenu and L. Kopp, "Optimality of high-resolution array processing using the eigensystem approach," IEEE Trans. ASSP-31, no. 5, pp. 1235-1248, Oct. 1983.
    • (1983) IEEE Trans. , vol.ASSP-31 , Issue.5 , pp. 1235-1248
    • Bienvenu, G.1    Kopp, L.2
  • 15
    • 0022683359 scopus 로고
    • Multiple emitter location and signal parameter estimation
    • NY 1979, reprinted in IEEE Trans, on Antenna and Propag., Mar.
    • R. O. Schmidt, "Multiple emitter location and signal parameter estimation," Proc. RADC Spectrum Estimation Workshop, NY 1979, reprinted in IEEE Trans, on Antenna and Propag., vol. AP-34, no. 3, pp. 276-280, Mar. 1986.
    • (1986) Proc. RADC Spectrum Estimation Workshop , vol.AP-34 , Issue.3 , pp. 276-280
    • Schmidt, R.O.1
  • 17
    • 0022794413 scopus 로고
    • Esprit, a subspace rotation approach to estimation of parameters of cisoids in noise
    • Oct.
    • R. Roy, A. Paulraj and T. Kailath, "Esprit, a subspace rotation approach to estimation of parameters of cisoids in noise," IEEE Trans, on ASSP, vol. ASSP-34, no. 5, pp. 1340-1342, Oct. 1986.
    • (1986) IEEE Trans, on ASSP , vol.ASSP-34 , Issue.5 , pp. 1340-1342
    • Roy, R.1    Paulraj, A.2    Kailath, T.3
  • 18
    • 84948589801 scopus 로고
    • An array processing technique using the first principal component
    • SVD and Signal Processing, M. Deprettere, Ed. Amsterdam, The Netherlands: North Holland
    • P. Comon, "An array processing technique using the first principal component," in SVD and Signal Processing, M. Deprettere, Ed. Amsterdam, The Netherlands: North Holland, 1988.
    • (1988)
    • Comon, P.1
  • 19
    • 0003601995 scopus 로고
    • ESPRIT–Estimation of Signal Paramaters via Rotational Invariance Techniques
    • Ph.D. Thesis, Stanford University, Aug.
    • R. Roy, "ESPRIT–Estimation of Signal Paramaters via Rotational Invariance Techniques," Ph.D. Thesis, Stanford University, Aug. 1987.
    • (1987)
    • Roy, R.1
  • 20
    • 0024702515 scopus 로고
    • ESRIT–Estimation of Signal Parameters via Rotational Invariance Techniques
    • July
    • R. Roy, and T. Kailath, "ESRIT–Estimation of Signal Parameters via Rotational Invariance Techniques," IEEE Trans. ASSP, vol. 37, no. 7, pp. 984-995, July 1989.
    • (1989) IEEE Trans. ASSP , vol.37 , Issue.7 , pp. 984-995
    • Roy, R.1    Kailath, T.2
  • 23
    • 0003352969 scopus 로고
    • Adaptive algorithm for estimating eigenvectors of correlation-type matrices
    • San Diego
    • J. Karhunen, "Adaptive algorithm for estimating eigenvectors of correlation-type matrices," in Proc. ICASSP, San Diego, 1984, pp. 14.6.1-14.6.4.
    • (1984) Proc. ICASSP , pp. 14.6.1-14.6.4
    • Karhunen, J.1
  • 24
    • 84948602968 scopus 로고
    • An 0(n2 log n) method for finding the eigenvalues of a symmetric Toepliz and Han-kel matrices
    • preprint, Jan
    • D. Pal, A. Ligtenberg and T. Kailath, "An 0(n2 log n) method for finding the eigenvalues of a symmetric Toepliz and Han-kel matrices," preprint, Jan 1987.
    • (1987)
    • Pal, D.1    Ligtenberg, A.2    Kailath, T.3
  • 26
    • 0020140899 scopus 로고
    • Least squares type algorithm for adaptive implementation of Pisarenko’s harmonic retrieval method
    • V. U. Reddy, B. E. Gardt and T. Kailath, "Least squares type algorithm for adaptive implementation of Pisarenko’s harmonic retrieval method," IEEE ASSP, vol. 30, no. 3, pp. 399-405,1982.
    • (1982) IEEE ASSP , vol.30 , Issue.3 , pp. 399-405
    • Reddy, V.U.1    Gardt, B.E.2    Kailath, T.3
  • 28
    • 0022665581 scopus 로고
    • Estimating the covariance matrix by signal sub-space averaging
    • Feb.
    • I. Karasalo, "Estimating the covariance matrix by signal sub-space averaging," IEEE Trans, on ASSP, vol. 34, no. 1, pp. 8-12, Feb. 1986.
    • (1986) IEEE Trans, on ASSP , vol.34 , Issue.1 , pp. 8-12
    • Karasalo, I.1
  • 29
    • 84948589490 scopus 로고
    • Fast computation of a restricted subset of eigen-pairs of a varying hermitian matrix
    • Signal Processing and Parallel Processing, Aug. 1-12, Leuven, Belgium.
    • P. Comon, "Fast computation of a restricted subset of eigen-pairs of a varying hermitian matrix," in Proc. NATO ASI on Numerical Linear Algebra, Signal Processing and Parallel Processing, Aug. 1-12, 1988, Leuven, Belgium.
    • (1988) Proc. NATO ASI on Numerical Linear Algebra
    • Comon, P.1
  • 30
    • 0001070999 scopus 로고
    • Some modified matrix eigenvalue problems
    • Apr.
    • G. H. Golub, "Some modified matrix eigenvalue problems," SIAM Review, vol. 15, no. 2, pp. 318-334, Apr. 1973.
    • (1973) SIAM Review , vol.15 , Issue.2 , pp. 318-334
    • Golub, G.H.1
  • 31
    • 34250270918 scopus 로고
    • Updating the singular value decomposition
    • J. R. Bunch, C. P. Nielsen, "Updating the singular value decomposition," Numerische Math., vol. 31, pp. 111-129, 1978.
    • (1978) Numerische Math. , vol.31 , pp. 111-129
    • Bunch, J.R.1    Nielsen, C.P.2
  • 35
    • 84948596294 scopus 로고    scopus 로고
    • Parametric methods for spatial signal processing in the presence of unknown colored noise fields
    • to appear in IEEE Trans. ASSP.
    • J. P. Lecadre, "Parametric methods for spatial signal processing in the presence of unknown colored noise fields," to appear in IEEE Trans. ASSP.
    • Lecadre, J.P.1
  • 36
    • 0024055271 scopus 로고
    • Focusing matrices for coherent sig-nal-subspace processing
    • Aug.
    • H. Hung and M. Kaveh, "Focusing matrices for coherent sig-nal-subspace processing," IEEE Trans. ASSP, pp. 1272-1281, Aug. 1988.
    • (1988) IEEE Trans. ASSP , pp. 1272-1281
    • Hung, H.1    Kaveh, M.2
  • 37
    • 84966204836 scopus 로고
    • Methods for modifying matrix factorizations
    • Apr.
    • P. E. Gill, G. H. Golub,W. Murray, and M.A. Saunders,"Methods for modifying matrix factorizations," Math. Comp., vol. 28, no. 126, pp. 505-535, Apr. 1974.
    • (1974) Math. Comp. , vol.28 , Issue.126 , pp. 505-535
    • Gill, P.E.1    Golub, G.H.2    Murray, W.3    Saunders, M.A.4
  • 38
    • 0017348174 scopus 로고
    • Numerical comparison of Kaiman filter algorithms: orbit determination case study
    • G. J. Bierman and C. Thornton, "Numerical comparison of Kaiman filter algorithms: orbit determination case study," Automatica, vol. 13, pp. 23-35, 1977.
    • (1977) Automatica , vol.13 , pp. 23-35
    • Bierman, G.J.1    Thornton, C.2
  • 39
    • 0019049862 scopus 로고
    • Alternatives in discrete-time recursive estimation
    • Also reprinted in Lectures on Wiener and Kaiman Filtering, T. Kailath, Ed. New York, NY: Springer-Verlag, 1981.
    • T. Kailath, "Alternatives in discrete-time recursive estimation," Int. Jour. Control, 1980, vol. 32, no. 2, pp. 311-328. Also reprinted in Lectures on Wiener and Kaiman Filtering, T. Kailath, Ed. New York, NY: Springer-Verlag, 1981.
    • (1980) Int. Jour. Control , vol.32 , Issue.2 , pp. 311-328
    • Kailath, T.1
  • 40
    • 0001560241 scopus 로고
    • Numerical aspects of different Kaiman filter implementations
    • Oct.
    • M. Verhaegen and P. Van Dooren, "Numerical aspects of different Kaiman filter implementations," IEEE Trans. on AC, vol. 31, no. 10, pp. 907-917, Oct. 1986.
    • (1986) IEEE Trans. on AC , vol.31 , Issue.10 , pp. 907-917
    • Verhaegen, M.1    Van Dooren, P.2
  • 41
    • 0023247028 scopus 로고
    • A Fast QR frequency-domain RLS adaptive filter
    • Apr.
    • J. M. Cioffi, A Fast QR frequency-domain RLS adaptive filter," Proc. ICASSP, Dallas, Apr. 1987, vol. 1, pp. 407-410.
    • (1987) Proc. ICASSP, Dallas , vol.1 , pp. 407-410
    • Cioffi, J.M.1
  • 42
  • 43
    • 33747738463 scopus 로고
    • Singular value decomposition and least squares solutions
    • or Handbook of Automatic Computation, Wilkinson and Reinsch, Ed. New York, NY: Springer-Verlag, 1971.
    • C. H. Colub and C. Reinsch, "Singular value decomposition and least squares solutions," Numerische Math, vol. 14, pp. 403-420, 1970, or Handbook of Automatic Computation, Wilkinson and Reinsch, Ed. New York, NY: Springer-Verlag, 1971.
    • (1970) Numerische Math , vol.14 , pp. 403-420
    • Colub, C.H.1    Reinsch, C.2
  • 45
    • 84948606309 scopus 로고    scopus 로고
    • Advances in principal component signal processing
    • M. Deprettere Ed. Amsterdam, The Netherlands: North Holland.
    • R. J. Vaccaro et al., "Advances in principal component signal processing," First Workshop on SVD and Signal Processing, M. Deprettere Ed. Amsterdam, The Netherlands: North Holland.
    • First Workshop on SVD and Signal Processing
    • Vaccaro, R.J.1
  • 46
    • 0346498507 scopus 로고
    • The calculation of specified eigenvectors by inverse iteration
    • Linear Algebra. Handbook for Automatic Computation, J. H. Wilkinson and C. Reinsch, Eds. New York, NY: Springer-Verlag
    • G. Peters and J. H. Wilkinson, "The calculation of specified eigenvectors by inverse iteration," in Linear Algebra. Handbook for Automatic Computation, J. H. Wilkinson and C. Reinsch, Eds. New York, NY: Springer-Verlag, 1971.
    • (1971)
    • Peters, G.1    Wilkinson, J.H.2
  • 47
    • 0022794411 scopus 로고
    • Implementation of adaptive array algorithms
    • Oct.
    • R.Schreiber,"Implementation of adaptive array algorithms," IEEE Trans. ASSP, vol. 34, no. 5, pp. 1038-1045, Oct. 1986.
    • (1986) IEEE Trans. ASSP , vol.34 , Issue.5 , pp. 1038-1045
    • Schreiber, R.1
  • 48
    • 0002316189 scopus 로고
    • Rank one modification of symmetric eigenproblem
    • J. R. Bunch, C. P. Nielsen, and D. C. Sorensen, "Rank one modification of symmetric eigenproblem," Numerische Math., vol. 31, pp. 31-48, 1978.
    • (1978) Numerische Math. , vol.31 , pp. 31-48
    • Bunch, J.R.1    Nielsen, C.P.2    Sorensen, D.C.3
  • 49
    • 0014751986 scopus 로고
    • The rotation of eigenvectors by a perturbation
    • C. Davis and W. Kahan, "The rotation of eigenvectors by a perturbation," SIAM Jour. Num. Anal., vol. 7, pp. 1-46, 1970.
    • (1970) SIAM Jour. Num. Anal. , vol.7 , pp. 1-46
    • Davis, C.1    Kahan, W.2
  • 50
    • 0016896723 scopus 로고
    • The behavior of eigenvalues and singular values under perturbations of restricted rank
    • R. C. Thompson, "The behavior of eigenvalues and singular values under perturbations of restricted rank," Linear Algebra and its Applications, vol. 13, pp. 69-78, vol. 13, 1976.
    • (1976) Linear Algebra and its Applications , vol.13 , Issue.13 , pp. 69-78
    • Thompson, R.C.1
  • 51
    • 0022276831 scopus 로고
    • Remarks on matrix eigenvalue computations
    • S. Y. Kung, H.J. White-house, and T. Kailath Eds. Englewood Cliffs, NJ: Prentice-Hall
    • B. N. Parlett, "Remarks on matrix eigenvalue computations," in VLSI and Modern Signal Processing, S. Y. Kung, H.J. White-house, and T. Kailath Eds. Englewood Cliffs, NJ: Prentice-Hall, 1985.
    • (1985) VLSI and Modern Signal Processing
    • Parlett, B.N.1
  • 52
    • 0001288470 scopus 로고
    • Accuracy and effectiveness of the Lanczos algorithm for the symmetric eigenproblem
    • C. C. Paige, "Accuracy and effectiveness of the Lanczos algorithm for the symmetric eigenproblem," Linear Algebra and its Applications, vol. 34, pp. 235-258, 1980.
    • (1980) Linear Algebra and its Applications , vol.34 , pp. 235-258
    • Paige, C.C.1
  • 54
    • 84968486060 scopus 로고
    • On estimating the largest eigenvalue with Lanczos algorithm
    • Jan.
    • B. N. Parlett, H. Simon, and L. M. Stringer, "On estimating the largest eigenvalue with Lanczos algorithm," Mathematics of Computation, vol. 36, no. 157, pp. 153-165, Jan. 1982.
    • (1982) Mathematics of Computation , vol.157 , Issue.36 , pp. 153-165
    • Parlett, B.N.1    Simon, H.2    Stringer, L.M.3
  • 55
    • 84948597485 scopus 로고
    • Adaptive computation of a few extreme eigen-pairs of a positive definite hermitian matrix
    • Sept. 5-8, Grenoble, France.
    • P. Comon, "Adaptive computation of a few extreme eigen-pairs of a positive definite hermitian matrix," Proc. of EUSIPCO, Sept. 5-8,1988, Grenoble, France.
    • (1988) Proc. of EUSIPCO
    • Comon, P.1
  • 56
    • 0000288016 scopus 로고
    • Calculating the singular values and pseudo inverse of a matrix
    • ser. B
    • G. H. Golub and W. Kahan, "Calculating the singular values and pseudo inverse of a matrix," SIAM Journal Num. Anal., ser. B, vol. 2, no. 2, pp. 205-224, 1965.
    • (1965) SIAM Journal Num. Anal. , vol.2 , Issue.2 , pp. 205-224
    • Golub, G.H.1    Kahan, W.2
  • 57
    • 0016036395 scopus 로고
    • Bidiagonalization of matrices and solution of linear equations
    • Mar.
    • C. C. Paige, "Bidiagonalization of matrices and solution of linear equations," SIAM Jour. Numer. Analysis, vol. 11, no. 1, Mar. 1974.
    • (1974) SIAM Jour. Numer. Analysis , vol.11 , Issue.1
    • Paige, C.C.1
  • 58
    • 0019576431 scopus 로고
    • A block lanczos method for computing the singular values and corresponding singular vectors of a matrix
    • June
    • G. H. Golub, F. T. Luk, and M. L. Overton, "A block lanczos method for computing the singular values and corresponding singular vectors of a matrix," ACM Trans. Math. Soft, pp. 149-169, June 1981.
    • (1981) ACM Trans. Math. Soft , pp. 149-169
    • Golub, G.H.1    Luk, F.T.2    Overton, M.L.3
  • 59
    • 0023588731 scopus 로고
    • An incomplete factorization algorithm for adpative filtering
    • Dec.
    • P. Comon and D. Trystram, "An incomplete factorization algorithm for adpative filtering," Signal Processing, vol. 13, no. 4, pp. 353-360, Dec. 1987.
    • (1987) Signal Processing , vol.13 , Issue.4 , pp. 353-360
    • Comon, P.1    Trystram, D.2
  • 60
    • 0020796539 scopus 로고
    • Adaptation convergence of spectral estimation based on Pisarenko harmonic retrieval
    • Aug.
    • M. G. Larimore, "Adaptation convergence of spectral estimation based on Pisarenko harmonic retrieval," IEEE Trans. ASSP, pp. 955-962, Aug. 1983.
    • (1983) IEEE Trans. ASSP , pp. 955-962
    • Larimore, M.G.1
  • 61
    • 0022185373 scopus 로고
    • Adaptive methods for real time Pisarenko spe trum estimate
    • Y. H. Hu, "Adaptive methods for real time Pisarenko spe trum estimate, in Proc. ICASSP 85, 1985, pp. 105-108.
    • (1985) Proc. ICASSP , vol.85 , pp. 105-108
    • Hu, Y.H.1
  • 62
    • 0022707111 scopus 로고
    • Adaptive spectral estimatic by the conjugate gradient method
    • H. Chen and T. K. Sarkar et al., "Adaptive spectral estimatic by the conjugate gradient method," IEEE Trans. ASSP, vol. 3 no. 2, pp. 272-284, 1986.
    • (1986) IEEE Trans. ASSP , vol.3 , Issue.2 , pp. 272-284
    • Chen, H.1    Sarkar, T.K.2
  • 63
    • 84939699437 scopus 로고
    • An iterative algorithm for locating the minimal eigenvector of a symmetric matrix
    • D. R. Fuhrmann and B. Liu, "An iterative algorithm for locating the minimal eigenvector of a symmetric matrix," in Pro ICASSP 84, 1984, pp. 45.8.1-45.8.4.
    • (1984) Pro ICASSP , vol.84 , pp. 45.8.1-45.8.4
    • Fuhrmann, D.R.1    Liu, B.2
  • 64
    • 0023963505 scopus 로고
    • Adaptive eigensubspace algorithms for direction or frequency estimation and tracking
    • Feb.
    • J. F.Yang and M. Kaveh, "Adaptive eigensubspace algorithms for direction or frequency estimation and tracking," IEEE, Trans. ASSP, vol. 36, no. 2, pp. 241-251, Feb. 1988.
    • (1988) IEEE, Trans. ASSP , vol.36 , Issue.2 , pp. 241-251
    • Yang, J.F.1    Kaveh, M.2
  • 65
    • 0017791094 scopus 로고
    • Adaptive data orthogonalization
    • N. L. Owsley, "Adaptive data orthogonalization," in Pro Conf. ICASSP, 1978, pp. 109-112.
    • (1978) Pro Conf. ICASSP , pp. 109-112
    • Owsley, N.L.1
  • 67
    • 0000288741 scopus 로고
    • An algorithm for subspace computatic with applications in signal processing
    • Apr.
    • D. R. Fuhrmann, "An algorithm for subspace computatic with applications in signal processing," SIAM Jour. Mati Anal. Appl., vol. 9, no. 2, Apr. 1988.
    • (1988) SIAM Jour. Mati Anal. Appl. , vol.9 , Issue.2
    • Fuhrmann, D.R.1
  • 68
    • 0022013023 scopus 로고
    • On stochastic approximation of tl eigenvectors and eigenvalues of the expectation of a rando matrix
    • Feb.
    • E. Oja and J. Karhunen, "On stochastic approximation of tl eigenvectors and eigenvalues of the expectation of a rando matrix," Journal of Math Analysis Appl., vol. 106, no. 1, p 69-84, Feb. 1985.
    • (1985) Journal of Math Analysis Appl. , vol.106 , Issue.1 , pp. 69-84
    • Oja, E.1    Karhunen, J.2
  • 69
    • 0023383912 scopus 로고
    • Limited precision effects in adaptive filtering
    • July
    • J. M. Cioffi, "Limited precision effects in adaptive filtering IEEE Trans. CAS, pp. 821-833, July 1987.
    • (1987) IEEE Trans. CAS , pp. 821-833
    • Cioffi, J.M.1
  • 70
    • 84948592418 scopus 로고    scopus 로고
    • An improved algorithm for computing the SVD ACM Trans
    • T. F.Chan, "An improved algorithm for computing the SVD ACM Trans. Math. Soft, vol. 8, pp. 84-88.
    • Math. Soft , vol.8 , pp. 84-88
    • Chan, T.F.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.