A new computational paradigm is described which o ers the possibility of superlinear (and sometimes unbounded) speedup, when parallel computation is used. The computations involved are subject only to given mathematical constraints and hence do not depend on external circumstances to achieve superlinear performance. The focus here is on geometric transformations. Given a geometric object A with...

We study the self-scaling BFGS method of Oren and Luenberger (1974) for solving unconstrained optimization problems. For general convex functions, we prove that the method is globally convergent with inexact line searches. We also show that the directions generated by the self-scaling BFGS method approach Newton's direction asymptotically. This would ensure superlinear convergence if, in additi...

The p-Laplacian Δpv ∇ · |∇v|p−2∇v arises from a variety of physical phenomena such as non-Newtonian fluids, reaction-diffusion problems, flow through porous media, nonlinear elasticity, glaciology, and petroleum extraction cf. Dı́az 1 . It is important to study the qualitative behavior e.g., oscillatory behavior of solutions of p-Laplace equations with superlinear terms and forcing terms. Forced...

A new computational paradigm is described which o ers the possibility of superlinear (and sometimes unbounded) speedup, when parallel computation is used. The computations involved are subject only to given mathematical constraints and hence do not depend on external circumstances to achieve superlinear performance. The focus here is on geometric transformations. Given a geometric object A with...

We investigate the relationship between patenting activity and the size of metropolitan areas in the United States over the last two decades (1980-2001). We find a clear superlinear effect, whereby patents are granted disproportionately in larger urban centers, thus showing increasing returns in inventing activity with respect to population size. We characterize this relation quantitatively as ...

Based on the identification of indices active at a solution of the mixed complementarity problem (MCP), we propose a class of Newton methods for which local superlinear convergence holds under extremely mild assumptions. In particular, the error bound condition needed for the identification procedure and the nondegeneracy condition needed for the convergence of the resulting Newton method are i...

In a variety of open source software projects, we document a superlinear growth of production intensity (R ~ c(β)) as a function of the number of active developers c, with a median value of the exponent β ≃ 4/3, with large dispersions of β from slightly less than 1 up to 3. For a typical project in this class, doubling of the group size multiplies typically the output by a factor 2(β) = 2.5, ex...