摘要
We present a numerical method for solving the indefinite least squares problem. We first normalize the coefficient matrix. Then we compute the hyperbolic QR factorization of the normalized matrix. Finally we compute the solution by solving several triangular systems. We give the first order error analysis to show that the method is backward stable. The method is more efficient than the backward stable method proposed by Chandrasekaran, Gu and Sayed.
We present a numerical method for solving the indefinite least squares problem. We first normalize the coefficient matrix. Then we compute the hyperbolic QR factorization of the normalized matrix. Finally we compute the solution by solving several triangular systems. We give the first order error analysis to show that the method is backward stable. The method is more efficient than the backward stable method proposed by Chandrasekaran, Gu and Sayed.
基金
Project partiallysupportedbytheNationalNaturalScienceFoundationofChina (GrantNo .0 3 14 42 7)andtheUniversityofKansasGeneralResearchFundAllocation (GrantNo .2 3 0 1717)
关键词
最小二乘问题
QR方法
因数分解
双曲问题
解答方法
indefinite least squares, hyperbolic rotation, ∑ p,q-orthogonal matrix, hyperbolic QR factorization, bidiagonal factorization, backward stability.
