On the theory and computation of nonperfect padé-hermite approximants

Cabay, Stan; Labahn, George; Beckermann, Bernhard

doi:10.1016/0377-0427(92)90206-d

Cited by 18 publications

(19 citation statements)

References 12 publications

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“…The NPHS is said to be normalized [9] if the nonsingularity condition III is replaced by r(0) = 1 and V (0) = I k . This can be achieved by multiplying S(z) on the right by Γ −1 , where…”

Section: Remarkmentioning

confidence: 99%

“…The nonsingularity condition III, namely γ = 0, refers to the nonsingularity of the associated striped Sylvester matrix M n defined in (1); in [9] it is shown that an exact NPHS exists iff M n is nonsingular.…”

Section: Remarkmentioning

confidence: 99%

“…is a numerical simultaneous Padé system (NSPS) [7,9] of type n for A * (z) if the following conditions are satisfied.…”

Section: Remarkmentioning

confidence: 99%

“…with C * (0) nonsingular, but the restriction to (9), which algebraically is made without loss of generality, permits us to establish in §3 a duality relationship between Padé-Hermite systems and simultaneous Padé systems.…”

Section: (Order Condition)mentioning

confidence: 99%

“…Padé-Hermite and simultaneous Padé systems [7,9] are approximants for the vector A t (z) = [a 0 (z), . .…”

mentioning

confidence: 99%

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Computation of Numerical Padé–Hermite and Simultaneous Padé Systems I: Near Inversion of Generalized Sylvester Matrices

Cabay¹,

Jones²,

Labahn³

1996

SIAM J. Matrix Anal. & Appl.

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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 Sylvester matrices. The inverse formulae provide good estimates for the condition numbers of these matrices, and serve as primary tools in a companion paper for the development of a fast, weakly stable algorithm for the computation of Padé-Hermite and simultaneous Padé systems and, thereby, also for the numerical inversion of striped and mosaic Sylvester matrices.

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Section: Remarkmentioning

confidence: 99%

Section: Remarkmentioning

confidence: 99%

“…is a numerical simultaneous Padé system (NSPS) [7,9] of type n for A * (z) if the following conditions are satisfied.…”

Section: Remarkmentioning

confidence: 99%

Section: (Order Condition)mentioning

confidence: 99%

“…Padé-Hermite and simultaneous Padé systems [7,9] are approximants for the vector A t (z) = [a 0 (z), . .…”

mentioning