Reverse aumulation and imploicit functions
Reverse aumulation and imploicit functions
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反向累积和内隐函数
DOI：
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发表时间：
1998
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影响因子：
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通讯作者：
B. Christianson
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作者：
B. Christianson
我们首先介绍一种简单的技术，利用反向积累的一阶导数的目标函数，包括在其结构的解的线性或非线性方程组。在线性情况下，对y求解Ay= b对应于伴随运算[bbar]:=[bbar]+vand [Abar]:=yv，其中对应于伴随方程vA= [ybar]的解。在非线性情况下，我们应用这些技术来获得计算函数值的自动数值误差估计。这些误差估计包括不准确的方程解以及舍入误差的影响。我们的基本技术可以推广到包含几个（线性或非线性）隐函数在其结构中的函数，无论是串行的还是嵌套的。在标量值目标函数的情况下，将方程解作为其构造的一部分。我们的算法所涉及的计算工作量最多与目标f的计算相同。
We begin by introducing a simple technique for using reverse accumulation the first derivatives of target functions which include in their construction the solution of systems of linear or nonlinear equations. In the linear case solving Ay= bfor ycorresponds to the adjoint operations [bbar]:=[bbar]+vand [Abar] :=yvwhere vis the solution to the adjoint equations vA= [ybar]. A more sophisticated construction applies in the nonlinear case We apply these technique to obtain automatic numerical error estimates for calculated function values. These error estimates include the effects of inaccurate equation solution as well as rounding error Our basic techiques can br generalized to functions which contain several (linear or nonlinear) implicit functions in their constuction, either serially or nested. In the case of scalar-valued target functions that include equation solution as part of their construction. Our algorithms involve at most the same order of computational effort as the computattion of the target f...