RELATIONSHIP BETWEEN THE STIFFLY WEIGHTEDPSEUDOINVERSE AND MULTI-LEVEL CONSTRAINED PSEUDOINVERSE  

作　　者：Mu-shengWei 

机构地区：[1]DepartmentofMathematics,EastChinaNormalUniversity,Shanghai200062,China

出　　处：《Journal of Computational Mathematics》2004年第3期427-436,共10页计算数学（英文）

摘　　要：It is known that for a given matrix A of rank r, and a set D of positive diagonal matrices, supw∈D‖（W^1/2A)+W^1/2‖ = (miniσ+(A^(i))^-1, in which (A^(i) is a submatrix of A formed with r = (rank(A)) rows of A, such that (A^(i) has full row rank r. In many practical applications this value is too large to be used. In this paper we consider the case that both A and W(∈D) are fixed with W severely stiff. We show that in this case the weighted pseudoinverse (W^1/2‖A)+W^1/2‖ is close to a multilevel constrained weighted pseudoinverse therefore ‖(W^1/2A)+W^1/‖2 is uniformly bounded.We also prove that in this case the solution set the stiffly weighted least squares problem is close to that of corresponding multi-level constrained least squares problem.

分 类 号：O151.21[理学—数学]