Least squares solution of F=PG with respect to positive semidefinite symmetric P is considered,a new necessary and sufficient condition for solvablity is given,and the expression of solution is derived in the some spe...Least squares solution of F=PG with respect to positive semidefinite symmetric P is considered,a new necessary and sufficient condition for solvablity is given,and the expression of solution is derived in the some special cases. Based on the expression, the least spuares solution of an inverse eigenvalue problem for positive semidefinite symmetric matrices is also given.展开更多
The main aim of this paper is to discuss the following two problems: Problem I: Given X ∈ Hn×m (the set of all n×m quaternion matrices), A = diag(λ1,…, λm) EEEEE Hm×m, find A ∈ BSHn×n≥such th...The main aim of this paper is to discuss the following two problems: Problem I: Given X ∈ Hn×m (the set of all n×m quaternion matrices), A = diag(λ1,…, λm) EEEEE Hm×m, find A ∈ BSHn×n≥such that AX = X(?), where BSHn×n≥ denotes the set of all n×n quaternion matrices which are bi-self-conjugate and nonnegative definite. Problem Ⅱ2= Given B ∈ Hn×m, find B ∈ SE such that ||B-B||Q = minAE∈=sE ||B-A||Q, where SE is the solution set of problem I , || ·||Q is the quaternion matrix norm. The necessary and sufficient conditions for SE being nonempty are obtained. The general form of elements in SE and the expression of the unique solution B of problem Ⅱ are given.展开更多
The tridiagonal coefficient matrix for the ＂fixed-fixed＂ spring-mass system was obtained by changing spring length. And then a new algorithm of the inverse problem was designed to construct the masses and the spring...The tridiagonal coefficient matrix for the ＂fixed-fixed＂ spring-mass system was obtained by changing spring length. And then a new algorithm of the inverse problem was designed to construct the masses and the spring constants from the natural frequencies of the ＂fixed-fixed＂ and ＂fixed-fres＂ spring-mass systems. An example was given to illustrate the results.展开更多
文摘Least squares solution of F=PG with respect to positive semidefinite symmetric P is considered,a new necessary and sufficient condition for solvablity is given,and the expression of solution is derived in the some special cases. Based on the expression, the least spuares solution of an inverse eigenvalue problem for positive semidefinite symmetric matrices is also given.
基金This work is supported by the NSF of China (10471039, 10271043) and NSF of Zhejiang Province (M103087).
文摘The main aim of this paper is to discuss the following two problems: Problem I: Given X ∈ Hn×m (the set of all n×m quaternion matrices), A = diag(λ1,…, λm) EEEEE Hm×m, find A ∈ BSHn×n≥such that AX = X(?), where BSHn×n≥ denotes the set of all n×n quaternion matrices which are bi-self-conjugate and nonnegative definite. Problem Ⅱ2= Given B ∈ Hn×m, find B ∈ SE such that ||B-B||Q = minAE∈=sE ||B-A||Q, where SE is the solution set of problem I , || ·||Q is the quaternion matrix norm. The necessary and sufficient conditions for SE being nonempty are obtained. The general form of elements in SE and the expression of the unique solution B of problem Ⅱ are given.
基金Project supported by the National Natural Science Foundation of China(Grant No.10271074)
文摘The tridiagonal coefficient matrix for the ＂fixed-fixed＂ spring-mass system was obtained by changing spring length. And then a new algorithm of the inverse problem was designed to construct the masses and the spring constants from the natural frequencies of the ＂fixed-fixed＂ and ＂fixed-fres＂ spring-mass systems. An example was given to illustrate the results.
