LEAST—SQUARES SOLUTIONS OF X^TAX=B OVER POSITIVE SEMIDEFINITE MATRIXES A
摘要
This paper is mainly concerned with solving the following two problems：Problem I.Given X∈R^n×m，B∈R^m×m.Find A∈Pn such that ‖X^T AX-B‖F=min,where Pn={A∈R^n×n|x^T Ax≥0,A↓x∈R^n}.Problem Ⅱ.Given A^～∈R^n×n.Find A^～∈SE such that‖A^～A^^‖F=minA∈SE‖A^～A‖F，where‖-‖F is Frobenius norm,and SE denotes the solution set of Problem I.The general solution of Problem I has been given.It is proved that there exists a unique solution for Problem Ⅱ.The expression of this solution for corresponding Problem Ⅱ for some special case will be derived.
引用本文（GB/T 7714）
DongxiuXie, LeiZhang. LEAST—SQUARES SOLUTIONS OF X^TAX=B OVER POSITIVE SEMIDEFINITE MATRIXES A[J]. Acta Scientiarum Naturalium Universitatis Sunyatseni, 2003.
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