USE OF QMR ALGORITHM TO CALCULATE VERY SLOW-MOTIONAL SPECTRA

使用 QMR 算法计算非常慢运动的光谱

• 批准号: 7602665
• 负责人: YUN-WEI CHIANG
• 金额: $ 0.12万
• 依托单位: CORNELL UNIVERSITY
• 依托单位国家: 美国
• 财政年份: 2007
• 资助国家: 美国
• 起止时间: 2007-09-01 至 2008-08-31
• 项目状态: 已结题
• 来源: https://reporter.nih.gov/project-details/7602665
• 关键词: Algorithms; Complex; Computer Retrieval of Information on Scientific Projects Database; Coupled; Equation; Funding; Grant; Institution; Methods; Monitor; Numbers; Research; Research Personnel; Residual state; Resources; Solutions; Source; Systemic Lupus Erythematosus; United States National Institutes of Health; programs; vector

This subproject is one of many research subprojects utilizing the resources provided by a Center grant funded by NIH/NCRR. The subproject and investigator (PI) may have received primary funding from another NIH source, and thus could be represented in other CRISP entries. The institution listed is for the Center, which is not necessarily the institution for the investigator. The diagonalization of the stochastic Liouville (SL) matrix using the Lanczos algorithm (LA) is optimized with the aid of the conjugate (CG) method for calculating 2D-ELDOR spectra in the slow-motional regime. In each step of the LA recursion, the convergence is monitored according to the residual norm calculated in the CG iterations. Thus the methods of the CG and LA can be coupled together to tri-diagonalize a large symmetric and complex sparse matrix efficiently. The LA-CG has been very successfully used to tri-diagonalize the SLE matrix in the slow-motional regime. However, due to the loss of orthogonality in the LA vectors, we found that the LA-CG method can break down in calculating spectra in the very slow-motional regime. This is mainly due to the fact that CG requires the residual norm to calculate the solution direction in each iteration. This indicates that the whole algorithm would be spoiled due to the loss of orthogonality after a certain number of LA projections. This would be particularly true when one calculates a very slow-motional spectrum that requires a large number of LA projections in order to adequately obtain good eigenvalues. The quasi-minimal residual (QMR), which was originally developed to be a linear equation solver, has been adapted for determining the number of LA projections in our program. In the QMR method, the solution vector is obtained by minimizing the quasi-residual norm, using QR factorization. It is of great advantage to us to replace CG with QMR to determine the number of LA projections, because the residual norm is NOT used iteratively as in the CG method to determine the solution direction in each iteration. Therefore, this LA-QMR method that we utilize provides an advantage of avoiding the breakdown noted above.

该副本是利用众多研究子项目之一 由NIH/NCRR资助的中心赠款提供的资源。子弹和 调查员（PI）可能已经从其他NIH来源获得了主要资金， 因此可以在其他清晰的条目中代表。列出的机构是 对于中心，这不一定是调查员的机构。 使用Lanczos算法（LA）的随机Liouville（SL）矩阵的对角化借助于慢速运动状态中计算2D-ELDOR光谱的方法进行了优化。在LA递归的每个步骤中，根据CG迭代中计算的残余规范来监测收敛性。因此，可以将CG和LA的方法耦合在一起，以有效地化大型对称和复杂的稀疏基质。 LA-CG非常成功地用于将SLE矩阵进行慢速计量状态的三对法化。 但是，由于LA载体的正交性丧失，我们发现LA-CG方法在计算非常缓慢的计量状态时可能会分解。这主要是由于CG需要剩余标准来计算每次迭代中的溶液方向。这表明由于一定数量的LA预测后正交性丧失，整个算法将被宠坏。当一个人计算出非常慢的电位光谱时，这将是尤其如此，该光谱需要大量的LA投影才能充分获得良好的特征值。 最初开发为线性方程求解器的准最低残留物（QMR）已改编成确定我们程序中LA投影的数量。在QMR方法中，通过使用QR分解来最大程度地降低准延迟规范来获得溶液矢量。用QMR替换CG以确定LA投影的数量对我们来说是一个很大的优势，因为剩余标准在CG方法中不迭代使用以确定每次迭代中的解决方案方向。因此，我们使用的这种LA-QMR方法提供了避免上述分解的优势。