A transpose-free two-sided nonsymmetric Lanczos method is developed for multiple starting vectors on both the left and right. The method is mathematically equivalent to the two-sided methods without look-ahead or deflation steps, but avoids the use of the transpose of the system matrix. The method is applied to the computation of the matrix Padé approximation to a linear dynamical system. The r...

We discuss the Padé approximation to the ππ scattering amplitudes in 1–loop chiral perturbation theory. The approximation restores unitarity and can reproduce the correct resonance poles, but the approximation violates crossing symmetry and produce spurious poles on the complex s plane and therefore plagues its predictions on physical quantities at quantitative level. However we find that one v...

In this paper, a belief propagation (BP) decoding algorithm via Tchebyshev-Padé approximation is proposed for low-density parity-check (LDPC) codes. Compared with the standard BP decoding algorithm, the proposed algorithm significantly reduces computational complexity without noticeable performance loss. The approximation error is also analyzed and it is demonstrated that this error is indeed v...

It is well-known that the denominators of Pade approximants can be considered as orthogonal polynomials with respect to a linear functional. This is usually shown by defining Pade -type approximants from so-called generating polynomials and then improving the order of approximation by imposing orthogonality conditions on the generating polynomials. In the multivariate case, a similar constructi...

We study a constructive method of rational approximation of analytic functions based on ideas of the theory of Hankel operators. Some properties of the corresponding Hankel operator are investigated. We also consider questions related to the convergence of rational approximants. Analogues of Montessus de Ballore’s and Gonchars’s theorems on the convergence of rows of Padé approximants are proved.

In univariate Padé approximation we learn from the Froissart phenomenon that Padé approximants to perturbed Taylor series exhibit almost cancelling pole–zero combinations that are unwanted. The location of these pole–zero doublets was recently characterized for rational functions by the so-called Froissart polynomial. In this paper the occurrence of the Froissart phenomenon is explored for the ...