Abstract:A novel approach, which uses the Levin transformations or the hybrid of the Levin transformations and summation-by-parts, is presented for the acceleration of the slowly convergent series that asymptotically behave as 1∕n k and sinusoidal functions divided by n k . This approach does not need the asymptotic expansion for the Green's functions and the Bessel functions, which saves the work for finding the asymptotic expansion coefficients. This approach has been applied to the acceleration of the infinite serie… Show more
“…Signal integrity primarily involves the electrical performance of the wires and other packaging structures used to move signals about within an electronic product. This topic is an important activity at all levels of electronics packaging and assembly, from internal connections of an IC, through the package, the printed circuit board (PCB), the backplane, and inter-system connections [2]. On PCBs, signal integrity becomes a serious concern when the transition times of signals start to become comparable to the propagation time across the board.…”
Section: Acknowledgementsmentioning
confidence: 99%
“…When u = v or w u = w v = w in (4.10), T 3 converges monotonically as 1/n. In this situation, the asymptotic expansion of T 3 can be written as cos(ξ/z) [77], where…”
This dissertation is dedicated to my beloved grandmother Tianying Dai and my parents, Zaolin Xu and Yimei Chen, whose affection, love, encouragement and prays of day and night make me able to get such success and honor. This dissertation is also in memory of my grandfather. The absence during the last moments of his life is my biggest regret in my PhD career.
“…Signal integrity primarily involves the electrical performance of the wires and other packaging structures used to move signals about within an electronic product. This topic is an important activity at all levels of electronics packaging and assembly, from internal connections of an IC, through the package, the printed circuit board (PCB), the backplane, and inter-system connections [2]. On PCBs, signal integrity becomes a serious concern when the transition times of signals start to become comparable to the propagation time across the board.…”
Section: Acknowledgementsmentioning
confidence: 99%
“…When u = v or w u = w v = w in (4.10), T 3 converges monotonically as 1/n. In this situation, the asymptotic expansion of T 3 can be written as cos(ξ/z) [77], where…”
This dissertation is dedicated to my beloved grandmother Tianying Dai and my parents, Zaolin Xu and Yimei Chen, whose affection, love, encouragement and prays of day and night make me able to get such success and honor. This dissertation is also in memory of my grandfather. The absence during the last moments of his life is my biggest regret in my PhD career.
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