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Volumn 429, Issue 8-9, 2008, Pages 2113-2130

Degeneration of structured integer matrices modulo an integer

Author keywords

Matrix inverse modulo an integer; Structured matrices

Indexed keywords

LINEAR SYSTEMS;

EID: 49249100712     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.laa.2008.06.020     Document Type: Article
Times cited : (11)

References (33)
  • 1
    • 0000081585 scopus 로고
    • Asymptotically fast solution of Toeplitz and related systems of linear equations
    • Bitmead R.R., and Anderson B.D.O. Asymptotically fast solution of Toeplitz and related systems of linear equations. Linear Algebra Appl. 34 (1980) 103-116
    • (1980) Linear Algebra Appl. , vol.34 , pp. 103-116
    • Bitmead, R.R.1    Anderson, B.D.O.2
  • 2
    • 34248585738 scopus 로고    scopus 로고
    • Decoding interleaved Reed-Solomon codes over noisy channels (special issue: selected papers from ICALP 2003)
    • Bleichenbacher D., Kiayias A., and Yung M. Decoding interleaved Reed-Solomon codes over noisy channels (special issue: selected papers from ICALP 2003). Theor. Comput. Sci. 379 3 (2007) 348-360
    • (2007) Theor. Comput. Sci. , vol.379 , Issue.3 , pp. 348-360
    • Bleichenbacher, D.1    Kiayias, A.2    Yung, M.3
  • 4
  • 5
    • 3042601667 scopus 로고
    • Distribution of bordered persymmetric matrices in a finite field
    • Daykin D.E. Distribution of bordered persymmetric matrices in a finite field. J. Reine und Angewandte Math. 203 (1960) 47-54
    • (1960) J. Reine und Angewandte Math. , vol.203 , pp. 47-54
    • Daykin, D.E.1
  • 6
    • 0001380055 scopus 로고
    • Exact solution of linear equations using p-adic expansions
    • Dixon J.D. Exact solution of linear equations using p-adic expansions. Numer. Math. 40 (1982) 137-141
    • (1982) Numer. Math. , vol.40 , pp. 137-141
    • Dixon, J.D.1
  • 7
    • 0000006297 scopus 로고
    • A probabilistic remark on algebraic program testing
    • Demillo R.A., and Lipton R.J. A probabilistic remark on algebraic program testing. Inform. Process. Lett. 7 4 (1978) 193-195
    • (1978) Inform. Process. Lett. , vol.7 , Issue.4 , pp. 193-195
    • Demillo, R.A.1    Lipton, R.J.2
  • 8
    • 0043198799 scopus 로고    scopus 로고
    • Fast inversion algorithms for a class of block structured matrices
    • Eidelman Y., and Gohberg I. Fast inversion algorithms for a class of block structured matrices. Contemp. Math. 281 (2001) 17-38
    • (2001) Contemp. Math. , vol.281 , pp. 17-38
    • Eidelman, Y.1    Gohberg, I.2
  • 9
    • 0034511243 scopus 로고    scopus 로고
    • W. Eberly, M. Giesbrecht, G. Villard, On computing the determinant and smith form of an integer matrix, in: Proceedings in the 41st Annual Symposium on Foundations of Computer Science (FOCS'2000), IEEE Computer Society Press, Los Alamitos, California, 2000, pp. 675-685.
    • W. Eberly, M. Giesbrecht, G. Villard, On computing the determinant and smith form of an integer matrix, in: Proceedings in the 41st Annual Symposium on Foundations of Computer Science (FOCS'2000), IEEE Computer Society Press, Los Alamitos, California, 2000, pp. 675-685.
  • 12
    • 84956252607 scopus 로고
    • The distribution of prime numbers
    • Karatsuba A.A. The distribution of prime numbers. Russian Math. Surveys 45 (1990) 99-171
    • (1990) Russian Math. Surveys , vol.45 , pp. 99-171
    • Karatsuba, A.A.1
  • 13
    • 0030395909 scopus 로고    scopus 로고
    • E. Kaltofen, A. Lobo, On rank properties of Toeplitz matrices over finite fields, in: Proceedings of International Symposium on Symbolic and Algebraic Computation (ISSAC'96), ACM Press, New York, 1996, pp. 241-249.
    • E. Kaltofen, A. Lobo, On rank properties of Toeplitz matrices over finite fields, in: Proceedings of International Symposium on Symbolic and Algebraic Computation (ISSAC'96), ACM Press, New York, 1996, pp. 241-249.
  • 14
    • 49249111938 scopus 로고    scopus 로고
    • M. Morf, Fast algorithms for multivariable systems, Ph.D. Thesis, Department of Electrical Engineering, Stanford University, Stanford, CA, 1974.
    • M. Morf, Fast algorithms for multivariable systems, Ph.D. Thesis, Department of Electrical Engineering, Stanford University, Stanford, CA, 1974.
  • 15
    • 0019146429 scopus 로고    scopus 로고
    • M. Morf, Doubling algorithms for Toeplitz and related equations, in: Proceedings of IEEE International Conference on ASSP, IEEE Press, Piscataway, New Jersey, 1980, pp. 954-959.
    • M. Morf, Doubling algorithms for Toeplitz and related equations, in: Proceedings of IEEE International Conference on ASSP, IEEE Press, Piscataway, New Jersey, 1980, pp. 954-959.
  • 16
    • 84945708089 scopus 로고
    • Approximate algorithms to derive exact solutions to systems of linear equations
    • Proceedings of EUROSAM, Springer, Berlin
    • Moenck R.T., and Carter J.H. Approximate algorithms to derive exact solutions to systems of linear equations. Proceedings of EUROSAM. Lecture Notes in Computer Science vol. 72 (1979), Springer, Berlin 63-73
    • (1979) Lecture Notes in Computer Science , vol.72 , pp. 63-73
    • Moenck, R.T.1    Carter, J.H.2
  • 18
    • 0032319031 scopus 로고    scopus 로고
    • V. Olshevsky, V.Y. Pan, A unified superfast algorithm for boundary rational tangential interpolation problem and for inversion and factorization of dense structured matrices, in: Proceedings of the 39th Annual IEEE Symposium on Foundation of Computer Science (FOCS 98), IEEE Computer Society Press, Los Alamitos, California, 1998, pp. 192-201.
    • V. Olshevsky, V.Y. Pan, A unified superfast algorithm for boundary rational tangential interpolation problem and for inversion and factorization of dense structured matrices, in: Proceedings of the 39th Annual IEEE Symposium on Foundation of Computer Science (FOCS 98), IEEE Computer Society Press, Los Alamitos, California, 1998, pp. 192-201.
  • 20
    • 49249099584 scopus 로고    scopus 로고
    • V.Y. Pan, Can we optimize Toeplitz/Hankel computations? in: E.W. Mayr, V.G. Ganzha, E.V. Vorozhtzov (Eds.), Proceedings of the Fifth International Workshop on Computer Algebra in Scientific Computing (CASC'02), Yalta, Crimea, September 2002, Technische Universität München, Germany, 2002, pp. 253-264.
    • V.Y. Pan, Can we optimize Toeplitz/Hankel computations? in: E.W. Mayr, V.G. Ganzha, E.V. Vorozhtzov (Eds.), Proceedings of the Fifth International Workshop on Computer Algebra in Scientific Computing (CASC'02), Yalta, Crimea, September 2002, Technische Universität München, Germany, 2002, pp. 253-264.
  • 21
    • 49249104237 scopus 로고    scopus 로고
    • V.Y. Pan, Nearly optimal Toeplitz/Hankel computations, Technical Reports 2002001, 2002002, and 2002017, Ph.D. Program in Computer Science, The Graduate Center, CUNY, New York, 2002. .
    • V.Y. Pan, Nearly optimal Toeplitz/Hankel computations, Technical Reports 2002001, 2002002, and 2002017, Ph.D. Program in Computer Science, The Graduate Center, CUNY, New York, 2002. .
  • 22
    • 49249133023 scopus 로고    scopus 로고
    • V.Y. Pan, On theoretical and practical acceleration of randomized computation of the determinant of an integer matrix, Zapiski Nauchnykh Seminarov POMI, vol. 316, St. Petersburg, Russia, 2004, pp. 163-187. (in English).
    • V.Y. Pan, On theoretical and practical acceleration of randomized computation of the determinant of an integer matrix, Zapiski Nauchnykh Seminarov POMI, vol. 316, St. Petersburg, Russia, 2004, pp. 163-187. (in English).
  • 23
    • 49249107617 scopus 로고    scopus 로고
    • V.Y. Pan, B. Murphy, R.E. Rosholt, X. Wang. Toeplitz and Hankel meet Hensel and Newton nearly optimal algorithms and their practical acceleration with saturated initialization, Technical Report 2004013, Ph.D. Program in Computer Science, The Graduate Center, CUNY, New York, 2004. .
    • V.Y. Pan, B. Murphy, R.E. Rosholt, X. Wang. Toeplitz and Hankel meet Hensel and Newton nearly optimal algorithms and their practical acceleration with saturated initialization, Technical Report 2004013, Ph.D. Program in Computer Science, The Graduate Center, CUNY, New York, 2004. .
  • 24
    • 49249118622 scopus 로고    scopus 로고
    • V.Y. Pan, B. Murphy, R.E. Rosholt, Unified nearly optimal algorithms for structured integer matrices and polynomials, Technical Report 2008003, Ph.D. Program in Computer Science, The Graduate Center, CUNY, New York, 2008. .
    • V.Y. Pan, B. Murphy, R.E. Rosholt, Unified nearly optimal algorithms for structured integer matrices and polynomials, Technical Report 2008003, Ph.D. Program in Computer Science, The Graduate Center, CUNY, New York, 2008. .
  • 25
    • 49249115034 scopus 로고    scopus 로고
    • V.Y. Pan, B. Murphy, R.E. Rosholt, Unified nearly optimal algorithms for structured integer matrices, Numerical Methods for Structured Matrices and Applications: Georg Heinig memorial volume, Birkhäuser Verlag, in press.
    • V.Y. Pan, B. Murphy, R.E. Rosholt, Unified nearly optimal algorithms for structured integer matrices, Numerical Methods for Structured Matrices and Applications: Georg Heinig memorial volume, Birkhäuser Verlag, in press.
  • 26
    • 84972540003 scopus 로고
    • Approximate formulas of some functions of prime numbers
    • Rosser J.B., and Schoenfeld L. Approximate formulas of some functions of prime numbers. Illinois J. Math. 6 (1962) 64-94
    • (1962) Illinois J. Math. , vol.6 , pp. 64-94
    • Rosser, J.B.1    Schoenfeld, L.2
  • 27
    • 84976779342 scopus 로고
    • Fast probabilistic algorithms for verification of polynomial identities
    • Schwartz J.T. Fast probabilistic algorithms for verification of polynomial identities. J. ACM 27 4 (1980) 701-717
    • (1980) J. ACM , vol.27 , Issue.4 , pp. 701-717
    • Schwartz, J.T.1
  • 28
    • 49249100079 scopus 로고    scopus 로고
    • Wang D., and Zhi L.-H. (Eds), Birkhäuser, Basel/Boston
    • In: Wang D., and Zhi L.-H. (Eds). Symbolic-Numeric Computation (2007), Birkhäuser, Basel/Boston
    • (2007) Symbolic-Numeric Computation
  • 29
    • 49249122253 scopus 로고    scopus 로고
    • J. Verschelde, S. Watt (Eds.), Proceedings of the Third International Workshop on Symbolic-Numeric Computation (SNC2007), July 2007, London, Ontario, Canada, ACM Press, New York, 2007.
    • J. Verschelde, S. Watt (Eds.), Proceedings of the Third International Workshop on Symbolic-Numeric Computation (SNC2007), July 2007, London, Ontario, Canada, ACM Press, New York, 2007.
  • 30
    • 49249090717 scopus 로고    scopus 로고
    • D.A. Bini, V.Y. Pan, J. Verschelde (Eds.), Theoretical Computer Science, Special Issue on Symbolic-Numerical Algorithms, in press.
    • D.A. Bini, V.Y. Pan, J. Verschelde (Eds.), Theoretical Computer Science, Special Issue on Symbolic-Numerical Algorithms, in press.
  • 31
  • 32
    • 49249092882 scopus 로고    scopus 로고
    • X. Wang, How frequently is the matrix nonsingular, Technical Report 2002018, Ph.D. Program in Computer Science, The Graduate Center, CUNY, New York, 2002.
    • X. Wang, How frequently is the matrix nonsingular, Technical Report 2002018, Ph.D. Program in Computer Science, The Graduate Center, CUNY, New York, 2002.
  • 33
    • 84925463455 scopus 로고
    • Probabilistic algorithms for sparse polynomials
    • Proceedings of EUROSAM'79, Springer, Berlin
    • Zippel R.E. Probabilistic algorithms for sparse polynomials. Proceedings of EUROSAM'79. Lecture Notes in Computer Science vol. 72 (1979), Springer, Berlin 216-226
    • (1979) Lecture Notes in Computer Science , vol.72 , pp. 216-226
    • Zippel, R.E.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.