A note on inversion of Toeplitz matrices

AbstractIt is shown that the invertibility of a Toeplitz matrix can be determined through the solvability of two standard equations. The inverse matrix can be denoted as a sum of products of circulant matrices and upper triangular Toeplitz matrices. The stability of the inversion formula for a Toeplitz matrix is also considered

An error bound for the MAOR method

AbstractSuppose Aχ = b is a system of linear equations where the matrix A is symmetric positive definite and consistently ordered. A bound for the norm of the errors εk = χ − χk of the MAOR method in terms of the norms of δk = χk − χk−1 and δk+1 = χk+1 − χk and their inner product is derived, ∥ϵk∥22≥1ω2{(|(w1 − 1)(w2 − 1)| + |w1(γ − w2)|μ22)2∥δk∥12 − 2(w1 − 1) 〈δk,δk+1〉 + 2|w1(ω − w2)|μ12∥δk∥2∥+∥δk+1∥2 + ∥δk+1∥22

Comparison results between Jacobi and other iterative methods

AbstractSome comparison results between Jacobi iterative method with the modified preconditioned simultaneous displacement (MPSD) iteration and other iterations, for solving nonsingular linear systems, are presented. It is showed that spectral radius of Jacobi iteration matrix B is less than that of several iteration matrices introduced in Liu (J. Numer. Methods Comput. Appl. 1 (1992) 58) under some conditions

Quasiparticle states around a nonmagnetic impurity in electron-doped iron-based superconductors with spin-density-wave order

The quasiparticle states around a nonmagnetic impurity in electron-doped iron-based superconductors with spin-density-wave (SDW) order are investigated as a function of doping and impurity scattering strength. In the undoped sample, where a pure SDW state exists, two impurity-induced resonance peaks are observed around the impurity site and they are shifted to higher (lower) energies as the strength of the positive (negative) scattering potential (SP) is increased. For the doped samples where the SDW order and the superconducting order coexist, the main feature is the existence of sharp in-gap resonance peaks whose positions and intensity depend on the strength of the SP and the doping concentration. In all cases, the local density of states exhibits clear $C_2$ symmetry. We also note that in the doped cases, the impurity will divide the system into two sublattices with distinct values of magnetic order. Here we use the band structure of a two-orbital model, which considers the asymmetry of the As atoms above and below the Fe-Fe plane. This model is suitable to study the properties of the surface layers in the iron-pnictides and should be more appropriate to describe the scanning tunneling microscopy experiments.Comment: 11 pages, 18 figure