递增 increase progressively; increase by degrees 人口的递增 a progressive increase in population; 产量与年递增。 the output increases progressively with years. 这所大学的注册人数比去年递增了10%。 the registration of the university shows an increase of 10 percent over last year.; 递增费用 progressive charges; 递增付款 progressive payment; 递增函数 increasing function; 递增序列 [数学] increasing sequence; ascending series
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Strictly increase monotonically 严格单调递增
One of its most important applications is to improve the optimization algorithms by evaluating the relevant derivatives information efficiently the aim of the work includes : to establish and study new algorithms - - cf - pcg algorithrns with ad ; to establish and study the extended cf - pcg algorithm ( ecfpcg ) . cf - pcg algorithms with ad is proposed on the basis of cf - pcg algorithms with sd , in addition to replace sd with ad , there are other significant modification to the algorithms . the results by theoretical analysis and numerical experiments implicate that cf - pcg algo - rithm with ad is an improvement to newton method with ad 论文首次将自动微分应用于牛顿- pcg型算法,构造了新算法,并从理论上比较了新算法与牛顿法的效率,证明了新算法的效率严格大于牛顿法的效率,而且新算法与牛顿法的效率比分别是问题维数n和目标函数复杂性的严格单调递增函数,当n趋于无穷大时,这个效率比的下界以ln ( n ) ln2的速率趋于无穷大。