20.500.12556/RUL-154375 Numerical methods for rectangular multiparameter eigenvalue problems, with applications to finding optimal ARMA and LTI models Standard multiparameter eigenvalue problems (MEPs) are systems of $k \ge 2$ linear $k$-parameter square matrix pencils. Recently, a new form of multipa-rameter eigenvalue problems has emerged: a rectangular MEP (RMEP) with only one multivariate rectangular matrix pencil, where we are looking for combinations of the parameters for which the rank of the pencil is not full. Applications include finding the optimal least squares autoregressive moving average (ARMA) model and the optimal least squares realization of autonomous linear time-invariant (LTI) dynamical system. For linear and polynomial RMEPs, we give the number of solutions and show how these problems can be solved numerically by a transformation into a standard MEP. For the transformation we provide new linearizations for quadratic multivariate matrix polynomials with a specific structure of monomials and consider mixed systems of rectangular and square multivariate matrix polynomials. This numerical approach seems computationally considerably more attractive than the block Macaulay method, the only other currently available numerical method for polynomial RMEPs. ARMA block Macaulay matrix LTI rectangular multiparameter eigenvalue problem standard multiparameter eigenvalue problem ARMA bločna Macaulayeva matrika pravokotni večparametrični problem lastnih vrednosti standardni večparametrični problem lastnih vrednosti true false true Angleški jezik Slovenski jezik Članek v reviji 2024-02-12 11:07:26 2024-02-12 11:07:31 2024-02-13 03:37:03 0000-00-00 00:00:00 2024 0 0 23 str. iss. 2, art. e2540 Vol. 31 2024 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 519.6 1070-5325 10.1002/nla.2540 172121859 Numerical_Linear_Algebra_App_-_2023_-_Hochstenbach_-_Numerical_methods_for_rectangular_multiparameter_eigenvalue_problems_.pdf Numerical_Linear_Algebra_App_-_2023_-_Hochstenbach_-_Numerical_methods_for_rectangular_multiparameter_eigenvalue_problems_.pdf 1 291A46F51CC332ED6D84C3297A220F7C 2af4eb7e5ce23cb14b4ae525881e89fbd505e7cd7e654579fa059799b3b7a833 d4a03835-c98e-11ee-a96a-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=180761 https://onlinelibrary.wiley.com/doi/10.1002/nla.2540 1 88e9b2ae-c98e-11ee-a96a-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=180760 Fakulteta za matematiko in fiziko 0 0 0