In this paper we consider the numerical solution of initial-value delay-differentialalgebraic equations (DDAEs) of retarded and neutral types, with a structure corresponding to that of Hessenberg DAEs. We give conditions under which the DDAE is well conditioned and show how the DDAE is related to an underlying retarded or neutral delay-ordinary differential equation (DODE). We present convergen...

GMRES is an iterative method that provides better solutions when dealing with larg linear systems of equations with unsymmetric coefficient matrix. By shifting the Arnoldi process to begin with Ar0 instead of r0, simpler GMRES implementation, proposed by Walker and Zhou in 1994, is obtained that in this method, an upper triangular problem is solved instead of hessenberg least square problem. Th...

Aggressive early deflation is a QR algorithm deflation strategy that takes advantage of matrix perturbations outside of the subdiagonal entries of the Hessenberg QR iterate. It identifies and deflates converged eigenvalues long before the classic small-subdiagonal strategy would. The new deflation strategy enhances the performance of conventional large-bulge multishift QR algorithms, but it is ...

In this paper, we present an algorithm for computing the characteristic polynomial of the pencil (A ? sE). It is shown that after a preliminary reduction of the matrices A and E to, respectively, an upper Hessenberg and an upper triangular matrix, the problem of computing the characteristic polynomial is transformed to the solution of certain triangular systems of linear algebraic equations. We...

below) a sequence of e.0. polynomials [SI S. V. Salehi and E. P. Ryan. “On optimal nonlinear feedback regulation of linear plants,” IEEE Trans. Auiomai. Contr., vol. AC-27, pp. 1260-1264, 1982. [ IO] J . Sandor and D. Williamson. “Design of nonlinear regulators for linear plants,” IEEE Truns. Automar. Conrr.. vol. AC-22. pp. 47-50, 1977. 1111 F. G. Shinsky, Process Control Syslems. 2nd ed. New ...

In this paper we consider a general sequence of orthogonal Laurent polynomials on the unit circle and we first study the equivalences between recurrences for such families and Szegő’s recursion and the structure of the matrix representation for the multiplication operator in Λ when a general sequence of orthogonal Laurent polynomials on the unit circle is considered. Secondly, we analyze the co...

We present a numerically stable way to compute oscillatory integrals of the form ∫ 1 −1 f(x)e iωg(x) dx. For each additional frequency, only a small, well-conditioned linear system with a Hessenberg matrix must be solved, and the amount of work needed decreases as the frequency increases. Moreover, we can modify the method for computing oscillatory integrals with stationary points. This is the ...

Based on the upper-triangular Hessenberg forms for descriptor linear systems and a method for right coprime factorization of descriptor linear systems using matrix elementary transformations, a simple, neat and numerically stable iterative formula for right coprime factorization of a regular singleinput descriptor linear system is proposed. This iterative formula gives directly the coefficients...

We propose a new parallelization scheme for the Hessenberg double shift QR algorithm. Our scheme allows software pipelining and communication latency hiding, and gives almost perfect load balance. An asymptotic parallelizing overhead analysis shows that our scheme attains the best possible scalability of the double shift QR algorithm, and that the overheads are less than the multishift algorith...

In this paper we carry over the Björck-Pereyra algorithm for solving Vandermonde linear systems to what we suggest to call Szegö-Vandermonde systems VΦ(x), i.e., polynomialVandermonde systems where the corresponding polynomial system Φ is the Szegö polynomials. The properties of the corresponding unitary Hessenberg matrix allow us to derive a fast O(n2) computational procedure. We present numer...