Triangulations and simplicial methods (Q1346640)

Chapter 1 (Introduction) contains, in particular, an interesting historical consideration. Fixed point theorems and applications (a pure exchange economy, a finite n-person normal form game, an exchange economy with linear production technologies, convex optimization and a balanced game without side payments) are included (Chapter 2). Existing triangulations of \(S^n\) of \(R^n\), of continuous refinement of grid sizes of \((0, 1]\times S^n\) are described in Chapter 3 as well as \(D_1\)-triangulations of \(R^n\). \(T_1\)-triangulations of the unit simplex are described in Chapter 4. The \(D_1\)-triangulation in variable dimension algorithms on the unit simplex and on the Euclidean space is the topic of Chapters 6 and 7. The \(D_3\)-triangulation (Chapter 8) and the \(D_2\)-triangulation (Chapter 9) for simplicial homotopy algorithms are also discussed.