Fraction-free Computation of Catrix Padé Systems
نویسندگان
چکیده
We present a fraction-free approach to the computation of matrix Padé systems. The method relies on determining a modified Schur complement for the coefficient matrices of the linear systems of equations that are associated to matrix Padé approximation problems. By using this modified Schur complement for these matrices we are able to obtain a fast hybrid fraction-free algorithm for their computation. The algorithm is general and requires no extra assumptions on its input.
منابع مشابه
Free Convection Flow and Heat Transfer of Nanofluids of Different Shapes of Nano-Sized Particles over a Vertical Plate at Low and High Prandtl Numbers
In this paper, free convection flow and heat transfer of nanofluids of differently-shaped nano-sized particles over a vertical plate at very low and high Prandtl numbers are analyzed. The governing systems of nonlinear partial differential equations of the flow and heat transfer processes are converted to systems of nonlinear ordinary differential equation through similarity transformations. T...
متن کاملFraction-Free Computation of Matrix Rational Interpolants and Matrix GCDs
We present a new set of algorithms for computation of matrix rational interpolants and one-sided matrix greatest common divisors. Examples of these interpolants include Padé approximants, Newton–Padé, Hermite–Padé, and simultaneous Padé approximants, and more generally M-Padé approximants along with their matrix generalizations. The algorithms are fast and compute all solutions to a given probl...
متن کاملAnalysis of Magneto-hydrodynamics Jeffery-Hamel Flow with Nanoparticles by Hermite-Padé Approximation
The combined effects of nanoparticle and magnetic field on the nonlinear Jeffery-Hamel flow are analyzed in the present study. The basic governing equations are solved analytically to nonlinear ordinary differential equation using perturbation method together with a semi-numerical analytical technique called Hermite- Padé approximation. The obtained results are well agreed with that of the Adom...
متن کاملFast Solution of Toeplitz Systems of Equations and Computation of Padé Approximants
We present two new algorithms, ADT and MDT, for solving order-n Toeplitz systems of linear equations Tz = b in time O(n log n) and space O(n). The fastest algorithms previously known, such as Trench’s algorithm, require time Ω(n2) and require that all principal submatrices of T be nonsingular. Our algorithm ADT requires only that T be nonsingular. Both our algorithms for Toeplitz systems are de...
متن کاملComputation of Numerical Padé-Hermite and Simultaneous Padé Systems I: Near Inversion of Generalized Sylvester Matrices
Abstract. We present new formulae for the “near” inverses of striped Sylvester and mosaic Sylvester matrices. The formulae assume computation over floating-point rather than exact arithmetic domains. The near inverses are expressed in terms of numerical Padé-Hermite systems and simultaneous Padé systems. These systems are approximants for the power series determined from the coefficients of the...
متن کامل