中文摘要：

研究Hilbert空间上一般多元线性问题的多项式易处理性．讨论利用有限个连续线性泛函值所构造的算法．基于相应算子的特征值，得到了一般多元线性问题具有多项式易处理性的充分必要条件．与以前的结果相比，本研究得到的判别法在形式上更加简洁．

英文摘要：

The polynomial tractability problems of general muhivariate linear problems defined over the Hilbert spaces are studied. By using the algorithms constructed by finite evaluations of continuous linear functionals, based on the eigenvalues of corresponding relational operators, the necessary and sufficient conditions for polynomial tractability of general multivari- ate linear problems are obtained. Compared with the previous resuhs, these criteria are more concise in form.