Thesis (PhD) -- Stellenbosch University, 2001. / ENGLISH ABSTRACT: A robust and efficient adaptive sampling algorithm for multivariate, multiple output rational interpolation models, based on convergents of Thiele-type branched continued fractions, is presented. A variation of the standard branched continued fraction method is proposed that uses approximation to establish a non-rectangular grid of support points. Starting with a low order interpolant, the technique systematically increases the order by optimally choosing new support points in the areas of highest error, until the desired accuracy is achieved. In this way, accurate surrogate models are established by a small number of support points, without assuming any a priori knowledge of the microwave structure under study. The technique is illustrated and evaluated on several passive microwave structures, however it is general enough to be applied to many modelling problems. / AFRIKAANSE OPSOMMING: 'n Robuuste en effektiewe aanpasbare monsternemingsalgoritme vir multi-veranderlike, multi-uittree rasionale interpolasiemodelle, gegrond op konvergente van Thiele vertakte volgehoue breukuitbreidings, word beskryf. 'n Variasie op die konvensionele breukuitbreidingsmetode word voorgestel, wat 'n nie-reghoekige rooster van ondersteuningspunte gebruik in die funksiebenadering. Met 'n lae orde interpolant as beginpunt, verhoog die algoritme stelselmatig die orde van die interpolant deur optimaal verbeterde ondersteuningspunte te kies waar die grootste fout voorkom, totdat die gewensde akuraatheid bereik word. Hierdeur word akkurate surrogaat modelle opgebou ten spyte van min inisiele ondersteuningspunte, asook sonder voorkennis van die mikrogolfstruktuur ter sprake. Die algoritme word gedemonstreer en geevalueer op verskeie passiewe mikrogolfstrukture, maar is veelsydig genoeg om toepassing te vind in meer algemene modelleringsprobleme.