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| Fältnamn | Indikatorer | Metadata |
|---|---|---|
| 000 | 03143nam a2200313 4500 | |
| 001 | oai:DiVA.org:umu-78987 | |
| 003 | SwePub | |
| 008 | 130730s1978 | |||||||||||000 ||eng| | |
| 024 | 7 | a https://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-789872 URI |
| 040 | a (SwePub)umu | |
| 041 | a engb eng | |
| 042 | 9 SwePub | |
| 072 | 7 | a vet2 swepub-contenttype |
| 072 | 7 | a dok2 swepub-publicationtype |
| 100 | 1 | a Gelfgren, Jan,d 1947-u Umeå universitet,Matematiska institutionen4 aut0 (Swepub:umu)jage0002 |
| 245 | 1 0 | a Multipoint Padé approximants used for piecewise rational interpolation and for interpolation to functions of Stieltjes' type |
| 264 | 1 | a Umeå :b Umeå universitet,c 1978 |
| 300 | a 14 s. | |
| 338 | a electronic2 rdacarrier | |
| 520 | a A multipoint Padë approximant, R, to a function of Stieltjes1 type is determined.The function R has numerator of degree n-l and denominator of degree n.The 2n interpolation points must belong to the region where f is analytic,and if one non-real point is amongst the interpolation points its complex-conjugated point must too.The problem is to characterize R and to find some convergence results as n tends to infinity. A certain kind of continued fraction expansion of f is used.From a characterization theorem it is shown that in each step of that expansion a new function, g, is produced; a function of the same type as f. The function g is then used,in the second step of the expansion,to show that yet a new function of the same type as f is produced. After a finite number of steps the expansion is truncated,and the last created function is replaced by the zero function.It is then shown,that in each step upwards in the expansion a rational function is created; a function of the same type as f.From this it is clear that the multipoint Padê approximant R is of the same type as f.From this it is obvious that the zeros of R interlace the poles, which belong to the region where f is not analytical.Both the zeros and the poles are simple. Since both f and R are functions of Stieltjes ' type the theory of Hardy spaces can be applied (p less than one ) to show some error formulas.When all the interpolation points coincide ( ordinary Padé approximation) the expected error formula is attained. From the error formula above it is easy to show uniform convergence in compact sets of the region where f is analytical,at least wien the interpolation points belong to a compact set of that region.Convergence is also shown for the case where the interpolation points approach the interval where f is not analytical,as long as the speed qî approach is not too great. | |
| 650 | 7 | a NATURVETENSKAPx Matematik0 (SwePub)1012 hsv//swe |
| 650 | 7 | a NATURAL SCIENCESx Mathematics0 (SwePub)1012 hsv//eng |
| 653 | a Continued fractions | |
| 653 | a Hardy space | |
| 653 | a Padé approximant | |
| 653 | a series of Stieltjes | |
| 710 | 2 | a Umeå universitetb Matematiska institutionen4 org |
| 856 | 4 | u https://umu.diva-portal.org/smash/get/diva2:638352/FULLTEXT02.pdfx primaryx Raw objecty fulltext |
| 856 | 4 8 | u https://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-78987 |
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