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.

中文翻译：

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FEAST 特征值求解器 v4.0 用户指南

FEAST 库包代表了一个统一的框架，用于解决各种特征值问题系列，并在并行架构上实现准确性、鲁棒性、高性能和可扩展性。它的独创性在于对传统特征值算法设计的一种新的转换数值方法——FEAST 算法。该算法从复分析、数值线性代数和近似理论中收集关键元素，使用近似光谱投影仪构建最优子空间迭代技术。FEAST 可用于求解 Hermitian 或非 Hermitian 问题（线性或非线性）的标准形式和广义形式，它属于轮廓积分特征求解器系列。盛宴' 的主要计算任务包括数值求积计算，该计算涉及沿着复杂的轮廓求解独立的线性系统，每个系统都有多个右手边。在 v4.0 中，FEAST 已使用逆残差迭代算法重新实现，该算法能够以非常低的精度（单精度）求解线性系统，而不会影响 FEAST 双精度收敛速度。因此，使用新的默认优化参数时，v4.0 平均比 v2.1 和 v3.0 快 3-4 倍（自 2013 年以来，v2.1 已成为 Intel-MKL 的主要 HPC 特征求解器）。v4.0 还实现了新的重要功能，例如 IFEAST（使用不精确迭代求解器）、非线性多项式 FEAST 和具有 3-MPI 并行级别的 PFEAST。FEAST 既是一个综合性的库包，也是一个易于使用的软件。