This paper is concerned with a seque nce-lo-seque nce transformation s tudie d e xt e ns ive ly by Samuel Lubkin [J . R es. NBS 48, 228-254 (1952)1. Lubkin has studied the rate of con ve rgence of th e tra nsform ed seque nce, {Tn}, ve rs us the ori gin a l seque nce, {Sn }. In thi s respect, th e authors ha ve s hown tha t a more acc ura te evaluation of th e t ra nsform a tio n is achi eve d b y the compa ri son of {Tn} with {S"+I} in s tead of {Sn}. The ma in theore ms proved a re rate-o f- conv e rgence compari sons be tween {Tn} and {S" +I} wh e r e {SIl l is th e seque nce of pa rti al sums of a conve rgent seri es whose te rms are of const ant s ign or else are alte rnatin g. Key Word s: Conve rge nce accele ra ti on techniques; e ps il on·tra nsfo rm a ti on; nonlin ear seri es tra nsformati on; nume ri cal meth ods; seri es summa bilit y methods.
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