Abstract The periodic QR algorithm is a strongly backward stable method for computing the eigenvalues of products of matrices, or equivalently for computing the eigenvalues of block cyclic matrices. The main purpose of this paper is to show that this algorithm is numerically equivalent to the standard QR algorithm. It will be demonstrated how this connection may be used to develop a better unde...

This paper gives perturbation analyses of the Cholesky factorization with the form of perturbations we could expect from the equivalent backward error in A resulting from numerically stable computations. The analyses more accurately reflect the sensitivity of the problem than previous such results. Both numerical results and an analysis show the standard method of symmetric pivoting usually imp...

We consider two models commonly used in the literature to model adversarial injection of packets into a packet switching network. We establish the relation between these two types of models, and between them and the set of sequences of packets that allow stability. We also consider the adaptive setting in which packets are injected with only their source and destination but without a prescribed...

Non-standard backward heat conduction problem is ill-posed in the sense that the solution (if it exists) does not depend continuously on the data. In this paper, we propose a regularization strategy-quasi-reversibility method to analysis the stability of the problem. Meanwhile, we investigate the roles of regularization parameter in this method. Numerical result shows that our algorithm is effe...

An algorithm is introduced for the rapid evaluation at appropriately chosen nodes on the two-dimensional sphere S2 in R3 of functions specified by their spherical harmonic expansions (known as the inverse spherical harmonic transform), and for the evaluation of the coefficients in spherical harmonic expansions of functions specified by their values at appropriately chosen points on S2 (known as...

We investigate the robust stabilization problem for the descriptor discrete-time systems and build an optimal solution in the case when both the nominal system and the perturbations are given in terms of left coprime factorizations over RH∞. Numerically reliable solutions are given for both the stability radius and the associated controller, which, in addition, regain the same simplicity as in ...

A detailed structured backward error analysis for four kinds of Palindromic Polynomial Eigenvalue Problems (PPEP) ( d ∑ l=0 Alλ l ) x = 0, Ad−l = εA ⋆ l for l = 0, 1, . . . , ⌊d/2⌋, where ⋆ is one of the two actions: transpose and conjugate transpose, and ε ∈ {±1}. Each of them has its application background with the case ⋆ taking transpose and ε = 1 attracting a great deal of attention lately ...

Earlier work by Driscoll and Healy [4] has produced an efficient O(B log B) algorithm for computing the Fourier transform of band-limited functions on the 2-sphere. In this paper, we discuss an implementation of an O(B) algorithm for the numerical computation of Fourier transforms of functions defined on the rotation group, SO(3). This compares with the direct O(B) approach. The algorithm we im...

Uncertain partial differential equation is a type of partial differential equation driven by Liu processes. This paper first provides two methods for solving the first order linear uncertain partial differential equation and the inverse uncertainty distribution of solution is discussed. Moreover, on the basis of the study of uncertainty theory and the propagation process of internet public opin...

It is demonstrated that the method of steps for linear delay-differential equation together with the inverse Laplace transform can be used to find a converging sequence of polynomial approximants to the transcendental function determining stability of the delay equation. Numerical stability charts are shown to illustrate convergence. This approach can serve as a basis for an efficient numerical...