2024/01/31 by Wenhao Li, Zongyuan Han, Li, Wenhao +3
Computer Science · Physics and Astronomy · #65D32 #65F10 #65F15 #Electromagnetic Scattering and Analysis #FOS: Mathematics #Matrix Theory and Algorithms #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.2401.17757
openalex publication_date 2024/01/31 · openalex created_date 2024/02/02 · openalex updated_date 2026/07/28
The Golub-Welsch algorithm [ Math. Comp., 23: 221-230 (1969)] has long been assumed symmetric for estimating quadratic forms. Recent research indicates that asymmetric quadrature nodes may be more often and the existence of a practical symmetric quadrature for estimating matrix quadratic form is even doubtful.This paper derives a sufficient condition for symmetric quadrature nodes for estimating quadratic forms involving the Jordan-Wielandt matrices which frequently arise from many applications. The condition is closely related to how to construct an initial vector for the underlying Lanczos process. Applications of such constructive results are demonstrated by estimating the Estrada index in complex network analysis.