Open Science Research Excellence
@article{(International Science Index):http://waset.org/publications/4494,
  title    = {An Iterative Updating Method for Damped Gyroscopic Systems},
  author    = {Yongxin Yuan},
  country   = {China},
  institution={Hubei Normal University},
  abstract  = {The problem of updating damped gyroscopic systems using measured modal data can be mathematically formulated as following two problems. Problem I: Given Ma ∈ Rn×n, Λ = diagλ1, ··· , λp ∈ Cp×p, X = [x1, ··· , xp] ∈ Cn×p, where p<n and both Λ and X are closed under complex conjugation in the sense that λ2j = λ¯2j−1 ∈ C, x2j = ¯x2j−1 ∈ Cn for j = 1, ··· , l, and λk ∈ R, xk ∈ Rn for k = 2l + 1, ··· , p, find real-valued symmetric matrices D,K and a real-valued skew-symmetric matrix G (that is, GT = −G) such that MaXΛ2 + (D + G)XΛ + KX = 0. Problem II: Given real-valued symmetric matrices Da, Ka ∈ Rn×n and a real-valued skew-symmetric matrix Ga, find (D, ˆ G, ˆ Kˆ ) ∈ SE such that Dˆ −Da2+Gˆ−Ga2+Kˆ −Ka2 = min(D,G,K)∈SE (D−
Da2 + G − Ga2 + K − Ka2), where SE is the solution set of Problem I and · is the Frobenius norm. This paper presents an iterative algorithm to solve Problem I and Problem II. By using the proposed iterative method, a solution of Problem I can be obtained within finite iteration steps in the absence of roundoff errors, and the minimum Frobenius norm solution of Problem I can be obtained by choosing a special kind of initial matrices. Moreover, the optimal approximation solution (D, ˆ G, ˆ Kˆ ) of Problem II can be obtained by finding the minimum Frobenius norm solution of a changed Problem I. A numerical example shows that the introduced iterative algorithm is quite efficient.
},
  {International Journal of Mathematical and Computational Sciences },  volume    = {4},
  number    = {7},
  year      = {2010},
  pages     = {799 - 807},
  ee        = {http://waset.org/publications/4494},
  url       = {http://waset.org/Publications?p=43},
  bibsource = {http://waset.org/Publications},
  issn      = {eISSN:1307-6892},
  publisher = {World Academy of Science, Engineering and Technology},
  index     = {International Science Index 43, 2010},
}