Journal of Convex Analysis 16 (2009), No. 3, 779--790
Copyright Heldermann Verlag 2009
Numerical Computation of Fitzpatrick Functions
Bryan Gardiner
Dept. of Computer Science, I. K. Barber School of Arts and Sciences, University of British Columbia, 3333 University Way, Kelowna BC V1V 1V7, Canada
Yves Lucet
Dept. of Computer Science, I. K. Barber School of Arts and Sciences, University of British Columbia, 3333 University Way, Kelowna BC V1V 1V7, Canada
yves.lucet@ubc.ca
Fitzpatrick functions provide insights into the structure of operators. To help understand their information, we investigate their efficient numerical computation on a grid for operators with finite graphs defined on the real line. Our algorithms take advantage of existing computational Convex Analysis frameworks to improve previous worst-case time complexity results from quartic to quadratic. We also provide a linear-time algorithm for the computation of antiderivatives based on the Fitzpatrick function of infinite order.
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