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Volumn 28, Issue 3, 2006, Pages 829-844

Asymptotically optimal lower bounds for the condition number of a real vandermonde matrix

Author keywords

Chebyshev polynomials; Optimal condition number; Vandermonde matrix

Indexed keywords

ABSOLUTE VALUES; CHEBYSHEV POLYNOMIALS; LOWER BOUNDS; VANDERMONDE MATRIX;

EID: 34547223980     PISSN: 08954798     EISSN: 10957162     Source Type: Journal    
DOI: 10.1137/060652737     Document Type: Article
Times cited : (13)

References (18)
  • 2
    • 0034415996 scopus 로고    scopus 로고
    • The condition number of real Vandermonde, Krylov and positive definite Hankel matrices
    • B. BECKERMANN, The condition number of real Vandermonde, Krylov and positive definite Hankel matrices, Numer. Math., 85 (2000), pp. 553-577.
    • (2000) Numer. Math , vol.85 , pp. 553-577
    • BECKERMANN, B.1
  • 3
    • 84968468488 scopus 로고
    • Solution of Vandermonde systems of equations
    • A. BJÖRCK AND V. PEREYRA, Solution of Vandermonde systems of equations, Math. Comp., 24 (1970), pp. 893-903.
    • (1970) Math. Comp , vol.24 , pp. 893-903
    • BJÖRCK, A.1    PEREYRA, V.2
  • 5
    • 0033633262 scopus 로고    scopus 로고
    • Accurate singular value decompositions of structured matrices
    • J. DEMMEL, Accurate singular value decompositions of structured matrices, SIAM J. Matrix Anal. Appl., 21 (1999), pp. 562-580.
    • (1999) SIAM J. Matrix Anal. Appl , vol.21 , pp. 562-580
    • DEMMEL, J.1
  • 6
    • 0000205473 scopus 로고
    • On inverses of Vandermonde and confluent Vandermonde matrices
    • W. GAUTSCHI, On inverses of Vandermonde and confluent Vandermonde matrices, Numer. Math., 4 (1962), pp. 117-123.
    • (1962) Numer. Math , vol.4 , pp. 117-123
    • GAUTSCHI, W.1
  • 7
    • 0000082767 scopus 로고
    • Norm estimates for inverses of Vandermonde matrices
    • W. GAUTSCHI, Norm estimates for inverses of Vandermonde matrices, Numer. Math., 23 (1975), pp. 337-347.
    • (1975) Numer. Math , vol.23 , pp. 337-347
    • GAUTSCHI, W.1
  • 8
    • 0039576150 scopus 로고
    • Optimally conditioned Vandermonde matrices
    • W. GAUTSCHI, Optimally conditioned Vandermonde matrices, Numer. Math., 24 (1975), pp. 1-12.
    • (1975) Numer. Math , vol.24 , pp. 1-12
    • GAUTSCHI, W.1
  • 9
    • 0012061790 scopus 로고
    • On inverses of Vandermonde and confluent Vandermonde matrices III
    • W. GAUTSCHI, On inverses of Vandermonde and confluent Vandermonde matrices III, Numer. Math., 29 (1978), pp. 445-450.
    • (1978) Numer. Math , vol.29 , pp. 445-450
    • GAUTSCHI, W.1
  • 10
    • 0000846903 scopus 로고
    • HOW (un)stable are Vandermonde systems?
    • Asymptotic and Computational Analysis, R. Wong, ed, Dekker, New York
    • W. GAUTSCHI, HOW (un)stable are Vandermonde systems?, in Asymptotic and Computational Analysis, R. Wong, ed., Lecture Notes in Pure and Appl. Math. 124, Dekker, New York, 1990, pp. 193-210.
    • (1990) Lecture Notes in Pure and Appl. Math , vol.124 , pp. 193-210
    • GAUTSCHI, W.1
  • 11
    • 0000835513 scopus 로고
    • Lower bounds for the condition number of Vandermonde matrices
    • W. GAUTSCHI AND G. INGESE, Lower bounds for the condition number of Vandermonde matrices, Numer. Math., 52 (1988), pp. 241-250.
    • (1988) Numer. Math , vol.52 , pp. 241-250
    • GAUTSCHI, W.1    INGESE, G.2
  • 16
    • 0040076561 scopus 로고
    • Norms of certain matrices with applications to variations of the spectra of matrices and matrix pencils
    • R.-C LI, Norms of certain matrices with applications to variations of the spectra of matrices and matrix pencils, Linear Algebra Appl., 182 (1993), pp. 199-234.
    • (1993) Linear Algebra Appl , vol.182 , pp. 199-234
    • LI, R.-C.1
  • 17
    • 33749585513 scopus 로고    scopus 로고
    • Asymptotically Optimal Lower Bounds for the Condition Number of a Real Vandermonde Matrix
    • Technical report 2004-05, Department of Mathematics, University of Kentucky, Lexington, KY, Available at
    • R.-C. LI, Asymptotically Optimal Lower Bounds for the Condition Number of a Real Vandermonde Matrix, Technical report 2004-05, Department of Mathematics, University of Kentucky, Lexington, KY, 2004. Available at http://www.ms.uky.edu/~math/MAreport/.
    • (2004)
    • LI, R.-C.1
  • 18
    • 33750885730 scopus 로고    scopus 로고
    • Lower bounds for the condition number of a real confluent Vandermonde matrix
    • to appear
    • R.-C. LI, Lower bounds for the condition number of a real confluent Vandermonde matrix, Math. Comp., (2006), to appear.
    • (2006) Math. Comp
    • LI, R.-C.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.