메뉴 건너뛰기




Volumn 74, Issue 252, 2005, Pages 1777-1791

Algorithms for hyperbolic quadratic eigenvalue problems

Author keywords

Cyclic reduction; Overdamping condition; Quadratic eigenvalue problem; Quadratic matrix equation; Solvent

Indexed keywords


EID: 27144525204     PISSN: 00255718     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0025-5718-05-01748-5     Document Type: Article
Times cited : (47)

References (21)
  • 1
    • 0026837159 scopus 로고
    • Overdamped and gyroscopic vibrating systems
    • MR1176288 (93f:70021)
    • L. Barkwell and P. Lancaster, Overdamped and gyroscopic vibrating systems, Trans. ASME J. Appl. Mech. 59 (1992), 176-181. MR1176288 (93f:70021)
    • (1992) Trans. ASME J. Appl. Mech. , vol.59 , pp. 176-181
    • Barkwell, L.1    Lancaster, P.2
  • 2
    • 0002706262 scopus 로고
    • Gyroscopically stabilized systems: A class of quadratic eigenvalue problems with real spectrum
    • MR1152665 (93a:47015)
    • L. Barkwell, P. Lancaster, and A. S. Markus, Gyroscopically stabilized systems: a class of quadratic eigenvalue problems with real spectrum, Canad. J. Math. 44 (1992), 42-53. MR1152665 (93a:47015)
    • (1992) Canad. J. Math. , vol.44 , pp. 42-53
    • Barkwell, L.1    Lancaster, P.2    Markus, A.S.3
  • 3
    • 31244432772 scopus 로고    scopus 로고
    • Computations with infinite Toeplitz matrices and polynomials
    • MR1878936 (2002m:65038)
    • D. A. Bini, L. Gemignani, and B. Meini, Computations with infinite Toeplitz matrices and polynomials, Linear Algebra Appl. 343-344 (2002), 21-61. MR1878936 (2002m:65038)
    • (2002) Linear Algebra Appl. , vol.343-344 , pp. 21-61
    • Bini, D.A.1    Gemignani, L.2    Meini, B.3
  • 4
    • 0001693314 scopus 로고
    • Numerical solution of a quadratic matrix equation
    • MR0622713 (82f:65036)
    • G. J. Davis, Numerical solution of a quadratic matrix equation, SIAM J. Sci. Stat. Comput. 2 (1981), 164-175. MR0622713 (82f:65036)
    • (1981) SIAM J. Sci. Stat. Comput. , vol.2 , pp. 164-175
    • Davis, J.1
  • 5
    • 0000472010 scopus 로고
    • Algorithms for solvents of matrix polynomials
    • MR0471278 (57:11015)
    • J. E. Dennis, Jr., J. F. Traub, and R. P. Weber, Algorithms for solvents of matrix polynomials, SIAM J. Numer. Anal. 15 (1978), 523-533. MR0471278 (57:11015)
    • (1978) SIAM J. Numer. Anal. , vol.15 , pp. 523-533
    • Dennis Jr., J.E.1    Traub, J.F.2    Weber, R.P.3
  • 6
    • 0000942136 scopus 로고
    • A minimax theory for overdamped networks
    • MR0069030 (16:979b)
    • R. J. Duffin, A minimax theory for overdamped networks, J. Rational Mech. Anal. 4 (1955), 221-233. MR0069030 (16:979b)
    • (1955) J. Rational Mech. Anal. , vol.4 , pp. 221-233
    • Duffin, R.J.1
  • 8
    • 0000843979 scopus 로고
    • Quadratic matrix polynomials with a parameter
    • MR0858906 (88e:47027)
    • I. Gohberg, P. Lancaster, and L. Rodman, Quadratic matrix polynomials with a parameter, Adv. Appl. Math. 7 (1986), 253-281. MR0858906 (88e:47027)
    • (1986) Adv. Appl. Math. , vol.7 , pp. 253-281
    • Gohberg, I.1    Lancaster, P.2    Rodman, L.3
  • 9
    • 2542480153 scopus 로고    scopus 로고
    • Numerical solution of a quadratic eigenvalue problem
    • MR2063362
    • C.-H. Guo, Numerical solution of a quadratic eigenvalue problem, Linear Algebra Appl. 385 (2004), 391-406. MR2063362
    • (2004) Linear Algebra Appl. , vol.385 , pp. 391-406
    • Guo, C.-H.1
  • 10
    • 0043092269 scopus 로고    scopus 로고
    • Elliptic and hyperbolic quadratic eigenvalue problems and associated distance problems
    • MR1997361 (2004g:15011)
    • Y. Hachez and P. Van Dooren, Elliptic and hyperbolic quadratic eigenvalue problems and associated distance problems, Linear Algebra Appl. 371 (2003), 31-44. MR1997361 (2004g:15011)
    • (2003) Linear Algebra Appl. , vol.371 , pp. 31-44
    • Hachez, Y.1    Van Dooren, P.2
  • 11
    • 0034288884 scopus 로고    scopus 로고
    • Numerical analysis of a quadratic matrix equation
    • MR1795295 (2001i:65054)
    • N. J. Higham and H.-M. Kim, Numerical analysis of a quadratic matrix equation, IMA J. Numer. Anal. 20 (2000), 499-519. MR1795295 (2001i:65054)
    • (2000) IMA J. Numer. Anal. , vol.20 , pp. 499-519
    • Higham, N.J.1    Kim, H.-M.2
  • 12
    • 84867975401 scopus 로고    scopus 로고
    • Bounds for eigenvalues of matrix polynomials
    • MR1942721 (2003k:15020)
    • N. J. Higham and F. Tisseur, Bounds for eigenvalues of matrix polynomials, Linear Algebra Appl. 358 (2003), 5-22. MR1942721 (2003k:15020)
    • (2003) Linear Algebra Appl. , vol.358 , pp. 5-22
    • Higham, N.J.1    Tisseur, F.2
  • 13
    • 31244435530 scopus 로고    scopus 로고
    • Detecting a definite Hermitian pair and a hyperbolic or elliptic quadratic eigenvalue problem, and associated nearness problems
    • MR1917487 (2003f:93047)
    • N. J. Higham, F. Tisseur, and P. M. Van Dooren, Detecting a definite Hermitian pair and a hyperbolic or elliptic quadratic eigenvalue problem, and associated nearness problems, Linear Algebra Appl. 351-352 (2002), 455-474. MR1917487 (2003f:93047)
    • (2002) Linear Algebra Appl. , vol.351-352 , pp. 455-474
    • Higham, N.J.1    Tisseur, F.2    Van Dooren, P.M.3
  • 14
    • 0041904514 scopus 로고
    • Factorization of selfadjoint quadratic matrix polynomials with real spectrum
    • MR1365446 (97b:15015)
    • I. Krupnik, A. Markus, and P. Lancaster, Factorization of selfadjoint quadratic matrix polynomials with real spectrum, Linear Multilinear Algebra 39 (1995), 263-272. MR1365446 (97b:15015)
    • (1995) Linear Multilinear Algebra , vol.39 , pp. 263-272
    • Krupnik, I.1    Markus, A.2    Lancaster, P.3
  • 15
    • 0003430842 scopus 로고    scopus 로고
    • Pergamon Press, Oxford, 1966, and 2nd Edition, Dover, MR1949393 (2003i:34016)
    • P. Lancaster, Lambda-matrices and vibrating systems, Pergamon Press, Oxford, 1966, and 2nd Edition, Dover, 2002. MR1949393 (2003i:34016)
    • (2002) Lambda-matrices and Vibrating Systems
    • Lancaster, P.1
  • 16
    • 0000017859 scopus 로고
    • Quadratic eigenvalue problems
    • P. Lancaster, Quadratic eigenvalue problems, Linear Algebra Appl. 150 (1991), 499-506.
    • (1991) Linear Algebra Appl. , vol.150 , pp. 499-506
    • Lancaster, P.1
  • 17
    • 0037623911 scopus 로고    scopus 로고
    • A wider class of stable gyroscopic systems
    • MR1994333 (2004g:70039)
    • P. Lancaster, A. S. Markus, and F. Zhou, A wider class of stable gyroscopic systems, Linear Algebra Appl. 370 (2003), 257-267. MR1994333 (2004g:70039)
    • (2003) Linear Algebra Appl. , vol.370 , pp. 257-267
    • Lancaster, P.1    Markus, A.S.2    Zhou, F.3
  • 19
    • 0036018019 scopus 로고    scopus 로고
    • -1A = Q
    • MR1898750 (2003c:15018)
    • -1A = Q, Math. Comp. 71 (2002), 1189-1204. MR1898750 (2003c:15018)
    • (2002) Math. Comp. , vol.71 , pp. 1189-1204
    • Meini, B.1
  • 20
    • 0000322706 scopus 로고
    • Implicit application of polynomial filters in a k-step Arnoldi method
    • MR1146670 (921:65076)
    • D. C. Sorensen, Implicit application of polynomial filters in a k-step Arnoldi method, SIAM J. Matrix Anal. Appl. 13 (1992), 357-385. MR1146670 (921:65076)
    • (1992) SIAM J. Matrix Anal. Appl. , vol.13 , pp. 357-385
    • Sorensen, D.C.1
  • 21
    • 0035359418 scopus 로고    scopus 로고
    • The quadratic eigenvalue problem
    • MR1861082 (20021:65042)
    • F. Tisseur and K. Meerbergen, The quadratic eigenvalue problem, SIAM Rev. 43 (2001), 235-286. MR1861082 (20021:65042)
    • (2001) SIAM Rev. , vol.43 , pp. 235-286
    • Tisseur, F.1    Meerbergen, K.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.