以下为句子列表：
英文: According to the filter matrix particularity, the filter equation was solved by using conjugate gradient method.
中文: 并根据滤波矩阵的特殊性，釆用共轭梯度法求解滤波方程。
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英文: In the image reconstruction based on optimization without constraint, the variable metric method, the steepest descent method, and conjugate gradient method were applied to image reconstruction to improve iterative efficiency and reconstructed quality, an
中文: 摘要在无约束最优化为基础的图像重建问题中，为了提高迭代效率以及重建图像质量，首次提出将变度量法应用到图像重建中。
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英文: On the basis of the analysis of the hypothesis in surface-consistent model, the conjugate gradient method is applied to decompose the seismic record in time domain in terms of the surface-consistent precondition and model.
中文: 摘要通过对地表一致性数学物理模型的前提条件进行剖析，合理地确定了反射振幅一致性校正模型，并依据该模型及其实现条件提出使用共轭梯度方法在时间域对地震记录进行谱分解处理。
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英文: The real-time obtainment of the components of projection matrix and the substitution of constant step for optimal step in the one-dimension search in conjugate gradient were adopted to ensure the equality of reconstructed image from incomplete projections
中文: 通过即时获取投影矩阵分量，以固定步长替代共轭梯度法中一维搜索最优迭代步长，在确保品质的同时缩短重建时间。
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英文: This paper presents a conjugate gradient method using restart strategy for solving trust region subproblems. And the convergence is proved. The numerical results show that this strategy is very effective.
中文: 摘要给出了用共轭梯度法解信赖域子问题的重新开始策略，并证明了方法的收敛性，数值结果表明该策略可以大大提高算法的收敛速度。
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