# 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: $$f(u) = A - ... 1answer 162 views ### Numerically Recovering Imaginary Part of Analytic Continuation from Real Part My situation. I have a function of a complex variable f(z) defined through a complicated integral. What I am interested in is the value of this function on the imaginary axis. I have numerical ... 3answers 126 views ### How to calculate \arg(z_1z_2\cdots z_n) to minimize results error? As in title, which method is the most optimal for numerical calculating value of: \arg(z_1z_2\cdots z_n)? Method 1: one can first calculate Z=z_1z_2\cdots z_n and then calculate \arg(Z). ... 0answers 67 views ### Complex Integral Equation Solution in MATLAB I need to solve an integral equation in the form:$$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 $$where A(z) distribution is known and we are ... 1answer 135 views ### Applicable solvers for nonlinear coupled PDEs I've been trying to find an applicable PDE solver for cases such as this: Although when dealing with stiff equations in the complex domain, applying existing packages has been problematic. I've ... 1answer 103 views ### Are there special methods for solving f'(z)=0 for analytic f? I am trying to solve a bunch of equations for the zeros of the derivative of an analytic function, and I would like to know if there exist methods that exploit this structure to provide better ... 1answer 762 views ### Complex Numerical Integration using GSL I want to program an integration routine in C++ using the GSL library but for complex functions. How should I split my integrand to apply the gsl_integration_qag function on it. Just integrate the ... 0answers 58 views ### Need a smart way to numerically take residues in a multidimensional integral I'm trying to do an integral of the form \int_C f(u,v) , where C is a set of contours in u and v. In particular, each variable's contour starts at -\infty+i \epsilon, goes around a branch ... 2answers 197 views ### Continuation procedure to solve for a 2D curve that satisfies f(x,y) = 0 I have some function of R^2, that must be numerically computed. For instance, I might be interested in a real-valued contour integral that begins from (x,y) = 0.$$ 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 ...