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Questions tagged [complex-analysis]

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Complex differentiation of linear solvers

I have a linear system $$Ax=b$$ which I'm solving approximately, and I need to take the frechet derivative of x with respect to z. Were I solving the problem exactly (either analytically or to machine ...
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Suppose we have a conformal mapping from the unit disk in the $\omega$ plane onto the exterior of a polygon in the $z$ plane. The Schwarz-Christoffel mapping in this case is defined as: $$f(u) = A - ... 1answer 156 views Numerically Recovering Imaginary Part of Analytic Continuation from Real Part My situation. I have a function of a complex variable f(z) defined through a complicated integral. What I am interested in is the value of this function on the imaginary axis. I have numerical ... 3answers 125 views How to calculate \arg(z_1z_2\cdots z_n) to minimize results error? As in title, which method is the most optimal for numerical calculating value of: \arg(z_1z_2\cdots z_n)? Method 1: one can first calculate Z=z_1z_2\cdots z_n and then calculate \arg(Z). ... 0answers 66 views Complex Integral Equation Solution in MATLAB I need to solve an integral equation in the form:$$A(z)+\int\limits^{z_2}_{z_1}B(z') \frac{z^N}{z^N-z'^N} \frac{e^{i\beta}}{|z|}\mathrm{d}z'=0 $$where A(z) distribution is known and we are ... 1answer 131 views Applicable solvers for nonlinear coupled PDEs I've been trying to find an applicable PDE solver for cases such as this: Although when dealing with stiff equations in the complex domain, applying existing packages has been problematic. I've ... 1answer 103 views Are there special methods for solving f'(z)=0 for analytic f? I am trying to solve a bunch of equations for the zeros of the derivative of an analytic function, and I would like to know if there exist methods that exploit this structure to provide better ... 1answer 737 views Complex Numerical Integration using GSL I want to program an integration routine in C++ using the GSL library but for complex functions. How should I split my integrand to apply the gsl_integration_qag function on it. Just integrate the ... 0answers 58 views Need a smart way to numerically take residues in a multidimensional integral I'm trying to do an integral of the form \int_C f(u,v) , where C is a set of contours in u and v. In particular, each variable's contour starts at -\infty+i \epsilon, goes around a branch ... 2answers 189 views Continuation procedure to solve for a 2D curve that satisfies f(x,y) = 0 I have some function of R^2, that must be numerically computed. For instance, I might be interested in a real-valued contour integral that begins from (x,y) = 0.$$ f(x,y) = \Re\left[\int_0^{x + iy}...
I have a complex surface (real dimension 2) in $\mathbb{C}^2$ with coordinates $(z,w)$ given explicitely: for any $\xi \in \mathbb{C}$ I know points $w(\xi)$ of intersection of surface with complex ...
I need to calculate the following integral: $${1\over 2\pi i} \int_C f(E) \, d E$$ $$f(E) = {\rm Tr}\,\left(({\bf h} + E)\,{\bf G}(E) \right)$$ Where $\bf h$ is a matrix (one particle kinetic and ...