Conformal mapping has been a familiar tool of science and engineering for generations. Determination of a conformal map from the unit disk onto the Jordan region is reduced to solving the Theodorsen equation, which is an integral equation for boundary correspondence functions. There are many methods for solving the Theodorsen equation. It is the goal of numerical conformal mapping to find metho...

We introduce principal differences analysis (PDA) for analyzing differences between high-dimensional distributions. The method operates by finding the projection that maximizes the Wasserstein divergence between the resulting univariate populations. Relying on the Cramer-Wold device, it requires no assumptions about the form of the underlying distributions, nor the nature of their inter-class d...

In this paper the convergence properties of the two-side successive over-relaxation (TSSOR) method of Weierstrass’ type is discussed. Initial conditions under which this method is divergent are stated. The main theorem generalizes some recent results concerning divergent properties of simultaneous methods for finding polynomial zeros. Let f(x) = x + an−1xn−1 + · · ·+ a1x+ a0 be a monic polynomi...

The improvement in AOR method for solving this system has been carried out by Hadjimos [1], Recently, Yao-Tang et al. [2], improved AOR method which has been developed by [1]. In this work, we construct a preconditioner to improve the Accelerated Over-relaxation (AOR) iterative method for solution of linear systems. We reduce the spectral radius of iterative matrix by multiplication of Precondi...

Despite its success, the delete relaxation has significant pitfalls. Recent work has devised the red-black planning framework, where red variables take the relaxed semantics (accumulating their values), while black variables take the regular semantics. Provided the red variables are chosen so that redblack plan generation is tractable, one can generate such a plan for every search state, and ta...

Abstract: Combining iterative schemes with suitable preconditioners may improve the rate of the convergence of the methods. However, the real difficulty lies in the construction of the correct preconditioners applied to the formulated schemes. In this paper, the Modified Explicit Decoupled Group Successive Over-Relaxation method is formulated to solve the two dimensional steady-state Navier-Sto...

For an n-variate order-d tensor A, define Amax := sup‖x‖2=1〈A, x ⊗d〉 to be the maximum value taken by the tensor on the unit sphere. It is known that for a random tensor with i.i.d. ±1 entries, Amax . √ n · d · log d w.h.p. We study the problem of efficiently certifying upper bounds on Amax via the natural relaxation from the Sum of Squares (SoS) hierarchy. Our results include: When A is a rand...

We present and study a homographic best approximation problem, which arises in the analysis of waveform relaxation algorithms with optimized transmission conditions. Its solution characterizes in each class of transmission conditions the one with the best performance of the associated waveform relaxation algorithm. We present the particular class of first order transmission conditions in detail...