منابع مشابه
Solving differential matrix Riccati equations by a piecewise-linearized method based on diagonal Padé approximants
Differential Matrix Riccati Equations (DMREs) appear in several branches of science such as applied Physics and Engineering. For example, these equations play a fundamental role in Control Theory, optimal control, filtering and estimation, decoupling and order reduction, etc. In this paper a new method based on a theorem proved in this paper is described for solving DMREs by a piecewise-lineari...
متن کاملPadé Approximants in Complex Points Revisited
In 1976, Chisholm et al. 1 published a paper concerning the location of poles and zeros of Padé approximants of ln 1 − z developed at the complex point ζ : ln 1 − z ln 1 − ζ − ∑∞ n 1 1/n z − ζ/1 − ζ . They claimed that all poles and zeros of diagonal Padé approximants n/n interlace on the cut z ζ t 1 − ζ , t ∈ 1,∞ . Unfortunately, this result is only partially true, for poles. Klarsfeld remarke...
متن کاملConvergence of Multipoint Padé-type Approximants
Let µ be a finite positive Borel measure whose support is a compact subset K of the real line and let I be the convex hull of K. Let r denote a rational function with real coefficients whose poles lie in C \ I and r(∞) = 0. We consider multipoint rational interpolants of the function f (z) = dµ(x) z − x + r(z), where some poles are fixed and others are left free. We show that if the interpolati...
متن کاملEvaluating Padé Approximants of the Matrix Logarithm
The inverse scaling and squaring method for evaluating the logarithm of a matrix takes repeated square roots to bring the matrix close to the identity, computes a Padé approximant, and then scales back. We analyze several methods for evaluating the Padé approximant, including Horner’s method (used in some existing codes), suitably customized versions of the Paterson– Stockmeyer method and Van L...
متن کاملAlgebraic properties of robust Padé approximants
For a recent new numerical method for computing so-called robust Padé approximants through SVD techniques, the authors gave numerical evidence that such approximants are insensitive to perturbations in the data, and do not have so-called spurious poles, that is, poles with a close-by zero or poles with small residuals. A black box procedure for eliminating spurious poles would have a major impa...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 1980
ISSN: 0022-247X
DOI: 10.1016/0022-247x(80)90157-2