2016/02/16 by Davide Palitta, Valeria Simoncini, Palitta, Davide +1 · 1 citation
Computer Science · Physics and Astronomy · #FOS: Mathematics #Matrix Theory and Algorithms #Model Reduction and Neural Networks #Numerical Analysis (math.NA) #Numerical Methods and Algorithms
paper · pdf · doi:10.48550/arxiv.1602.05033
openalex publication_date 2016/02/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the numerical treatment of large-scale Sylvester and Lyapunov equations,\nprojection methods require solving a reduced problem to check convergence. As\nthe approximation space expands, this solution takes an increasing portion of\nthe overall computational effort. When data are symmetric, we show that the\nFrobenius norm of the residual matrix can be computed at significantly lower\ncost than with available methods, without explicitly solving the reduced\nproblem. For certain classes of problems, the new residual norm expression\ncombined with a memory-reducing device make classical Krylov strategies\ncompetitive with respect to more recent projection methods. Numerical\nexperiments illustrate the effectiveness of the new implementation for standard\nand extended Krylov subspace methods.\n