论文标题
盛宴特征值求解器v4.0用户指南
FEAST Eigenvalue Solver v4.0 User Guide
论文作者
论文摘要
盛宴库包是一个统一的框架，用于解决各种特征值问题，并在并行体系结构上实现准确性，鲁棒性，高性能和可扩展性。它的独创性在于针对传统特征值算法设计的新的变革性数值方法 - 盛宴算法。该算法从复杂分析，数值线性代数和近似理论中收集了关键要素，并使用近似光谱投影仪构建最佳的子空间迭代技术。盛宴可用于解决Hermitian或非甲米语问题的标准形式和广义形式（线性或非线性），并且属于Cortour Enctigation Eigensolvers家族。盛宴的主要计算任务由数值正交计算组成，该计算涉及沿复杂轮廓求解独立的线性系统，每个系统都有多个右侧。在v4.0中，使用反向残差迭代算法重新完成了盛宴，该算法使线性系统的精度非常低（单一精确）溶液，而对盛宴的双重精度收敛速度没有影响。结果，使用新的默认优化参数，v4.0的平均比v2.1和v3.0快3-4倍（自2013年以来，v2.1作为英特尔-MKL的主HPC Eigensolver的特征）。 v4.0还实现了新的重要特征，例如ifeast（使用不精确的迭代求解器），非线性多项式盛宴，并具有其3-MPI的并行性水平。盛宴既是综合的图书馆套餐，又是易于使用的软件。它包括灵活的反向通信界面，并准备使用驱动程序界面进行密集，带和稀疏的系统。
The FEAST library package represents an unified framework for solving various family of eigenvalue problems and achieving accuracy, robustness, high-performance and scalability on parallel architectures. Its originality lies with a new transformative numerical approach to the traditional eigenvalue algorithm design - the FEAST algorithm. The algorithm gathers key elements from complex analysis, numerical linear algebra and approximation theory, to construct an optimal subspace iteration technique using approximate spectral projectors. FEAST can be used for solving both standard and generalized forms of the Hermitian or non-Hermitian problems (linear or non-linear), and it belongs to the family of contour integration eigensolvers. FEAST's main computational task consists of a numerical quadrature computation that involves solving independent linear systems along a complex contour, each with multiple right hand sides. In v4.0, FEAST has been reimplemented using an inverse residual iteration algorithm which enables the linear systems to be solved with very low accuracy (in single precision) with no impact on the FEAST double precision convergence rate. As a result, v4.0 is on average 3-4 times faster than v2.1 and v3.0 using new default optimization parameters (v2.1 has been featured as Intel-MKL's principal HPC eigensolver since 2013). v4.0 also implements new important features such as IFEAST (using Inexact Iterative solver), Non-linear polynomial FEAST, and PFEAST with its 3-MPI levels of parallelism. FEAST is both a comprehensive library package, and an easy to use software. It includes flexible reverse communication interfaces and ready to use driver interfaces for dense, banded and sparse systems.
