This paper shows that Cayley Transforms, which map Orthogonal and SkewSymmetric matrices, may be considered the extension to matrix field of the complex conformal mapping function f1(z) = 1− z 1 + x . Then, by using a set of real matrices which are, simultaneously, Orthogonal and Symmetric (the Ortho−Sym matrices), it similarly shows how to extend two complex conformal mapping functions (namely...

Abstract. An effective algorithm is presented for solving the Beltrami equation ∂f = μ ∂f in a planar disk. The algorithm involves no evaluation of singular integrals. The strategy, working in concentric rings, is to construct a piecewise linear μ-conformal mapping and then correct the image using a known algorithm for conformal mappings. Numerical examples are provided and the computational co...

In this paper we deal with a new technique for large data compression. Contour mapping of two dimensional objects is of fundamental importance in remote sensing and computer vision applications. We present extensive algorithms applied to polygonized, simply-connected contours and reproduce desired shapes using an innovative data compression technique based on conformal mapping. In a previous wo...

The theory of the convergence of Krylov subspace iterations for linear systems of equations (conjugate gradients, biconjugate gradients, GMRES, QMR, Bi-CGSTAB, and so on) is reviewed. For a computation of this kind, an estimated asymptotic convergence factor ρ ≤ 1 can be derived by solving a problem of potential theory or conformal mapping. Six approximations are involved in relating the actual...

Monte Carlo simulations of the two-dimensional XY model are performed in a square geometry with free and mixed fixed-free boundary conditions. Using a Schwarz-Christoffel conformal mapping, we deduce the exponent η of the order parameter correlation function and its surface equivalent η‖ at the Kosterlitz-Thouless transition temperature. The well known value η(TKT) = 1/4 is easily recovered eve...

In this work we demonstrate the advantages of conformal mapping methods for the design of capacitive sensor setups. If the setups are modeled appropriately, the respective Laplace equations can be solved utilizing conformal mapping methods. These methods yield the equations describing the electric field of the sensor setups. The field equations contain the distinct geometric properties of the s...