Abstract
A method analogous to the Aitken extrapolation is proposed to accelerate the convergence of sequences of real or complex numbers with asymptotic behavior EquationSource % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyzamaaBa% aaleaacaWGUbaabeaakiabgIKi7kaabogacaqGVbGaaeOBaiaaboha% caqG0bGaeyOiGC7aaebCaeaacaWGLbWaa0baaSqaaiaad6gaaeaaca% WGKbGaamOAaaaakiabgkHiTiaadQgaaSqaaiaadQgacqGH9aqpcaaI% XaaabaGaamOCaaqdcqGHpis1aaaa!4B8C! where e i is the error of the ith element of the sequence, d j≥1 for all 1≤j≤r, and ∑dj > 1. The R-order of the resulting sequences is computed using methods which are also of independent interest.
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References
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Meyer, R. Acceleration of Superlinearly Convergent Sequences. Journal of Optimization Theory and Applications 96, 655–665 (1998). https://doi.org/10.1023/A:1022668629365
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DOI: https://doi.org/10.1023/A:1022668629365