High-Performance Numerical Library for Solving Eigenvalue Problems
The FEAST eigensolver package is a free high-performance numerical library for solving the Hermitian and non-Hermitian eigenvalue problems, and obtaining all the eigenvalues and (right/left) eigenvectors within a given search interval or arbitrary domain in the complex plane. Its originality lies with a new transformative numerical approach to the traditional eigenvalue algorithm design - the FEAST algorithm. The algorithm takes its inspiration from the density-matrix representation and contour integration technique in quantum mechanics. It contains elements from complex analysis, numerical linear algebra and approximation theory, and it can be defined as an optimal subspace iteration method using approximate spectral projectors. FEAST's main building block is a numerical quadrature computation consisting of solving independent linear systems along a complex contour, each with multiple right hand sides. A Rayleigh-Ritz procedure is then used to generate a reduced dense eigenvalue problem orders of magnitude smaller than the original one. The FEAST eigensolver combines simplicity and efficiency and it offers many important capabilities for achieving high performance, robustness, accuracy, and scalability on parallel architectures.
