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A computational method for large‐scale differential symmetric Stein equation
Author(s) -
Güldoğan Dericioğlu Yaprak,
Kurulay Muhammet
Publication year - 2018
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5405
Subject(s) - mathematics , krylov subspace , generalized minimal residual method , scale (ratio) , residual , rank (graph theory) , projection (relational algebra) , differential equation , matrix (chemical analysis) , constant (computer programming) , subspace topology , low rank approximation , block (permutation group theory) , numerical analysis , mathematical analysis , mathematical optimization , iterative method , algorithm , combinatorics , computer science , materials science , hankel matrix , composite material , programming language , physics , quantum mechanics
We propose a numerical method for solving large‐scale differential symmetric Stein equations having low‐rank right constant term. Our approach is based on projection the given problem onto a Krylov subspace then solving the low dimensional matrix problem by using an integration method, and the original problem solution is built by using obtained low‐rank approximate solution. Using the extended block Arnoldi process and backward differentiation formula (BDF), we give statements of the approximate solution and corresponding residual. Some numerical results are given to show the efficiency of the proposed method.