3,649 research outputs found
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
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
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