This paper is concerned with the construction of circulant preconditioners for Toeplitz systems arising from a piecewise continuous generating function with sign changes. If the generating function is given, we prove that for any " > 0, only O(log N) eigenvalues of our preconditioned Toeplitz systems of size N N are not contained in ?1?"; ?1+"] 1?"; 1+"]. The result can be modiied for trigonome...

The Generalized Minimal Residual method (GMRES) is often used to solve a nonsymmetric linear system Ax = b. But its convergence analysis is a rather difficult task in general. A commonly used approach is to diagonalize A = XΛX−1 and then separate the study of GMRES convergence behavior into optimizing the condition number of X and a polynomial minimization problem over A’s spectrum. This artifi...

This paper concerns the use of a method for the solution of ill-conditioned linear systems. We show that the Generalized Minimum Residual Method (GMRES) in conjunction with a truncated singular value decomposition can beused to solve large nonsymmetric linear systems of equations which are nearly singular. Error bounds are given for the right s i n g u l a r v ectors and singular values compute...

for all #, y in 31 and all a in $. The constants relative to such a derivation are the elements of 3t that commute with d. We shall call an element b a d-integral if b~a for some element a in 31, that is, if the equation x' ~xd—dx*=b has a solution in 31. Clearly if a is a solution of this equation then the totality of solutions is the set {a+c} where c ranges over the set of d-constants. In a ...

The need to integrate cost into the early product definition process as an engineering parameter is addressed. The application studied is a fuselage panel that is typical for commercial transport regional jets. Consequently, a semi-empirical numerical analysis using reference data was coupled to model the structural integrity of thin-walled structures with regard to material failure and bucklin...