FEAST特征值求解器v4 .0用户指南
FEAST Eigenvalue Solver v4.0 User Guide
摘要：
FEAST库包代表了一个统一的框架，用于解决各种特征值问题，并在并行架构上实现准确性，鲁棒性，高性能和可扩展性。它的独创性在于一个新的变革性的数值方法，传统的特征值算法设计-FEAST算法。该算法集合了复分析、数值线性代数和逼近理论中的关键元素，利用近似谱投影器构造了一种最优子空间迭代技术。FEAST可用于解决标准和广义形式的埃尔米特或非埃尔米特问题（线性或非线性），它属于家庭的轮廓积分特征解。FEAST的主要计算任务包括数值求积计算，涉及沿着复杂轮廓求解独立的线性系统，每个系统具有多个右侧。在v4.0中，FEAST已使用逆残差迭代算法重新实现，该算法使线性系统能够以非常低的精度（单精度的）求解，而不会影响FEAST的双精度的收敛速度。因此，使用新的默认优化参数，v4.0平均比v2.1和v3.0快3-4倍（自2013年以来，v2.1一直是英特尔-MKL的主要HPC特征解算器）。v4.0还实现了新的重要功能，如IFEAST（使用不精确迭代求解器），非线性多项式FEAST和PFEAST及其3-MPI并行级别。FEAST既是一个全面的库包，也是一个易于使用的软件。它包括灵活的反向通信接口和可用于密集、带状和稀疏系统的驱动程序接口。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
