The Hierarchical Subspace Iteration Method for Laplace–Beltrami Eigenproblems

Sparse eigenproblems are important for various applications in computer graphics. The spectrum and eigenfunctions of the Laplace--Beltrami operator, example, fundamental methods shape analysis mesh processing. Subspace Iteration Method is a robust solver these problems. In practice, however, Lanczos schemes often faster. this paper, we introduce Hierarchical (HSIM), novel sparse that operates on hierarchy nested vector spaces. constructed such coarsest space all eigenpairs can be computed with dense eigensolver. HSIM uses as initialization iterates from coarse to fine over hierarchy. On each level, subspace iterations, initialized solution previous used approximate eigenpairs. This approach substantially reduces number iterations needed finest grid compared non-hierarchical Method. Our experiments show solve meshes faster than state-of-the-art based preconditioned conjugate gradients iterations.