منابع مشابه
Padé approximant related to the Wallis formula
Based on the Padé approximation method, in this paper we determine the coefficients [Formula: see text] and [Formula: see text] such that [Formula: see text] where [Formula: see text] is any given integer. Based on the obtained result, we establish a more accurate formula for approximating π, which refines some known results.
متن کاملRecursive Algorithms for the Matrix Padé Problem
Abstract. A matrix triangularization interpretation is given for the recursive algorithms computing the Padé approximants along a certain path in the Padé table, which makes it possible to unify all known algorithms in this field [5], [6]. For the normal Padé table, all these results carry over to the matrix Padé problem in a straightforward way. Additional features, resulting from the noncommu...
متن کاملRobust Padé Approximation via SVD
Padé approximation is considered from the point of view of robust methods of numerical linear algebra, in particular the singular value decomposition. This leads to an algorithm for practical computation that bypasses most problems of solution of nearly-singular systems and spurious pole-zero pairs caused by rounding errors; a Matlab code is provided. The success of this algorithm suggests that...
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...
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ژورنال
عنوان ژورنال: The Journal of the Acoustical Society of America
سال: 1993
ISSN: 0001-4966
DOI: 10.1121/1.406558