In this paper,the generalized inverse eigenvalue problem for the（P,Q）-conjugate matrices and the associated approximation problem are discussed by using generalized singular value decomposition（GSVD）.Moreover,the ...In this paper,the generalized inverse eigenvalue problem for the（P,Q）-conjugate matrices and the associated approximation problem are discussed by using generalized singular value decomposition（GSVD）.Moreover,the least residual problem of the above generalized inverse eigenvalue problem is studied by using the canonical correlation decomposition（CCD）.The solutions to these problems are derived.Some numerical examples are given to illustrate the main results.展开更多
is gained by deleting the k<sup>th</sup> row and the k<sup>th</sup> column （k=1,2,...,n） from T<sub>n</sub>.We put for-ward an inverse eigenvalue problem to be that:If we don’t k...is gained by deleting the k<sup>th</sup> row and the k<sup>th</sup> column （k=1,2,...,n） from T<sub>n</sub>.We put for-ward an inverse eigenvalue problem to be that:If we don’t know the matrix T<sub>1,n</sub>,but weknow all eigenvalues of matrix T<sub>1,k-1</sub>,all eigenvalues of matrix T<sub>k+1,k</sub>,and all eigenvaluesof matrix T<sub>1,n</sub> could we construct the matrix T<sub>1,n</sub>.Let μ<sub>1</sub>,μ<sub>2</sub>,…,μ<sub>k-1</sub>,μ<sub>k</sub>,μ<sub>k+1</sub>,…,μ<sub>n-1</sub>,展开更多
In this article,we discuss singular Hermitian matrices of rank greater or equal to four for an inverse eigenvalue problem.Specifically,we look into how to generate n by n singular Hermitian matrices of ranks four and ...In this article,we discuss singular Hermitian matrices of rank greater or equal to four for an inverse eigenvalue problem.Specifically,we look into how to generate n by n singular Hermitian matrices of ranks four and five from a prescribed spectrum.Numerical examples are presented in each case to illustrate these scenarios.It was established that given a prescribed spectral datum and it multiplies,then the solubility of the inverse eigenvalue problem for n by n singular Hermitian matrices of rank r exists.展开更多
The problem of best approximating, a given square complex matrix in the Frobenius norm by normal matrices under a given spectral restriction is considered. The ne cessary and sufficient condition for the solvability ...The problem of best approximating, a given square complex matrix in the Frobenius norm by normal matrices under a given spectral restriction is considered. The ne cessary and sufficient condition for the solvability of the problem is given. A numerical algorithm for solving the problem is provided and a numerical example is presented.展开更多
基金Supported by the Key Discipline Construction Project of Tianshui Normal University
文摘In this paper,the generalized inverse eigenvalue problem for the（P,Q）-conjugate matrices and the associated approximation problem are discussed by using generalized singular value decomposition（GSVD）.Moreover,the least residual problem of the above generalized inverse eigenvalue problem is studied by using the canonical correlation decomposition（CCD）.The solutions to these problems are derived.Some numerical examples are given to illustrate the main results.
基金Project 19771020 supported by National Science Foundation of China
文摘is gained by deleting the k<sup>th</sup> row and the k<sup>th</sup> column （k=1,2,...,n） from T<sub>n</sub>.We put for-ward an inverse eigenvalue problem to be that:If we don’t know the matrix T<sub>1,n</sub>,but weknow all eigenvalues of matrix T<sub>1,k-1</sub>,all eigenvalues of matrix T<sub>k+1,k</sub>,and all eigenvaluesof matrix T<sub>1,n</sub> could we construct the matrix T<sub>1,n</sub>.Let μ<sub>1</sub>,μ<sub>2</sub>,…,μ<sub>k-1</sub>,μ<sub>k</sub>,μ<sub>k+1</sub>,…,μ<sub>n-1</sub>,
文摘In this article,we discuss singular Hermitian matrices of rank greater or equal to four for an inverse eigenvalue problem.Specifically,we look into how to generate n by n singular Hermitian matrices of ranks four and five from a prescribed spectrum.Numerical examples are presented in each case to illustrate these scenarios.It was established that given a prescribed spectral datum and it multiplies,then the solubility of the inverse eigenvalue problem for n by n singular Hermitian matrices of rank r exists.
文摘The problem of best approximating, a given square complex matrix in the Frobenius norm by normal matrices under a given spectral restriction is considered. The ne cessary and sufficient condition for the solvability of the problem is given. A numerical algorithm for solving the problem is provided and a numerical example is presented.
