2023/06/06 by Stefan Güttel, Güttel, Stefan, Igor Simunec +1 · 6 citations
Computer Science · Engineering · Mathematics · #65F10 #65F50 #Algorithm #Arnoldi iteration #Basis (linear algebra) #Computer science #Current (fluid) #Dimension (graph theory) #FOS: Mathematics #Generalized minimal residual method #Heuristic #Iterative method #Mathematical optimization #Mathematics #Neural Networks and Applications #Numerical Analysis (math.NA) #Process (computing) #Projection (relational algebra) #Sketch #Sparse and Compressive Sensing Techniques #Stochastic Gradient Optimization Techniques
paper · pdf · doi:10.48550/arxiv.2306.03592
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2023/06/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A sketch-and-select Arnoldi process to generate a well-conditioned basis of a Krylov space at low cost is proposed. At each iteration the procedure utilizes randomized sketching to select a limited number of previously computed basis vectors to project out of the current basis vector. The computational cost grows linearly with the dimension of the Krylov space. The subset selection problem for the projection step is approximately solved with a number of heuristic algorithms and greedy methods used in statistical learning and compressive sensing.