TY - JOUR
T1 - Differentiation via Logarithmic Expansions
AU - Fu, Michael C.
AU - Heidergott, Bernd
AU - Leahu, Haralambie
AU - Vázquez-Abad, Felisa J.
PY - 2020/2/1
Y1 - 2020/2/1
N2 - In this note, we introduce a new finite difference approximation called the Black-Box Logarithmic Expansion Numerical Derivative (BLEND) algorithm, which is based on a formal logarithmic expansion of the differentiation operator. BLEND capitalizes on parallelization and provides derivative approximations of arbitrary precision, i.e., our analysis can be used to determine the number of terms in the series expansion to guarantee a specified number of decimal places of accuracy. Furthermore, in the vector setting, the complexity of the resulting directional derivative is independent of the dimension of the parameter.
AB - In this note, we introduce a new finite difference approximation called the Black-Box Logarithmic Expansion Numerical Derivative (BLEND) algorithm, which is based on a formal logarithmic expansion of the differentiation operator. BLEND capitalizes on parallelization and provides derivative approximations of arbitrary precision, i.e., our analysis can be used to determine the number of terms in the series expansion to guarantee a specified number of decimal places of accuracy. Furthermore, in the vector setting, the complexity of the resulting directional derivative is independent of the dimension of the parameter.
KW - directional derivative
KW - Finite difference algorithm
KW - numerical differentiation
KW - sensitivity analysis
KW - Taylor series expansions
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U2 - 10.1142/S0217595919500349
DO - 10.1142/S0217595919500349
M3 - Article
AN - SCOPUS:85080908974
VL - 37
SP - 1
EP - 5
JO - Asia-Pacific Journal of Operational Research
JF - Asia-Pacific Journal of Operational Research
SN - 0217-5959
IS - 1
M1 - 1950034
ER -
