{ "item_title" : "The Computation of Fixed Points and Applications", "item_author" : [" M. J. Todd "], "item_description" : "Fixed-point algorithms have diverse applications in economics, optimization, game theory and the numerical solution of boundary-value problems. Since Scarf's pioneering work56,57] on obtaining approximate fixed points of continuous mappings, a great deal of research has been done in extending the applicability and improving the efficiency of fixed-point methods. Much of this work is available only in research papers, although Scarf's book58] gives a remarkably clear exposition of the power of fixed-point methods. However, the algorithms described by Scarf have been super eded by the more sophisticated restart and homotopy techniques of Merrill8, 9] and Eaves and Saigal1,16]. To understand the more efficient algorithms one must become familiar with the notions of triangulation and simplicial approxi- tion, whereas Scarf stresses the concept of primitive set. These notes are intended to introduce to a wider audience the most recent fixed-point methods and their applications. Our approach is therefore via triangu- tions. For this reason, Scarf is cited less in this manuscript than his contri- tions would otherwise warrant. We have also confined our treatment of applications to the computation of economic equilibria and the solution of optimization problems. Hansen and Koopmans28] apply fixed-point methods to the computation of an invariant optimal capital stock in an economic growth model. Applications to game theory are discussed in Scarf56,58], Shapley59], and Garcia, Lemke and Luethi24]. Allgower1] and Jeppson31] use fixed-point algorithms to find many solutions to boundary-value problems.", "item_img_path" : "https://covers3.booksamillion.com/covers/bam/3/54/007/685/3540076859_b.jpg", "price_data" : { "retail_price" : "54.99", "online_price" : "54.99", "our_price" : "54.99", "club_price" : "54.99", "savings_pct" : "0", "savings_amt" : "0.00", "club_savings_pct" : "0", "club_savings_amt" : "0.00", "discount_pct" : "10", "store_price" : "" } }

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