Questions tagged [complex-arithmetic]
For questions about implementing and using complex arithmetic operations.
25 questions
0 votes
0 answers
43 views
solving an initial boundary value problem with the Schrodinger equation and the Dirichlet condition using the discrete Fourier transform
The boundary value problem is given: \begin{cases} \frac{\partial E}{\partial z} = \alpha\frac{\partial^{2}E }{\partial x^{2}}, -X/2\lt x\lt X/2, \alpha \in \mathbb{C}\\ E(0,z)=0, E(X,z)=0\\ E(x,0)=...
3 votes
1 answer
140 views
2x2 complex symmetric eigendecomposition - LAPACK subroutine CLAESY
Asking here because I searched the LAPACK user forums and found nothing. I have a problem that requires the computation of the eigendecomposition $A=A^T=Q \Lambda Q^T$ for the 2x2 complex symmetric ...
- 1,081
0 votes
1 answer
81 views
Finding best phase in least-squares manner
I have the following problem: $$argmin_{\vec{x},\phi}||A\vec{x}-\vec{y}e^{j\phi}||_2^2$$ Here, $x$ and $y$ are vectors and $\phi$ is a constant phase factor that applies to the all entries of $y$. I ...
- 23
1 vote
0 answers
75 views
Does the choice of a complex inner product affect Krylov methods?
As far as I understand there are two definitions of the complex inner product: $$(a,b) = b^H a$$ and $$(a,b) = a^H b$$ I know some linear algebra libraries such as BLAS and Eigen uses the second one. ...
-2 votes
1 answer
65 views
Simplification of complex amplitudes
In a previous answer the following identity was presented $$-i \vec \kappa \exp^{[i\vec \kappa \cdot (\vec r_j - \vec r_i)]} = -\vec \kappa \sin[\vec \kappa \cdot (\vec r_j - \vec r_i)] \, .$$ Why ...
- 101
1 vote
1 answer
113 views
Why does this implementation for Eisenstein integer pairs of Euclid's method for finding greatest common denominators get stuck for this one point?
My Math SE question determining if a coincident point in a pair of rotated hexagonal lattices is closest to the origin? explains the problem I have. I won't reproduce the whole thing in detail here, ...
- 1,152
2 votes
1 answer
576 views
Solving Schrodinger Equation with finite element and Crank-Nicolson?
I have asked this in Mathematic section, but received no reply. Please let me ask here to see if threr is any difference. The Schrodinger equation without potential has the following form: $$\...
- 119
4 votes
0 answers
248 views
Stable iterative solver for complex symmetric linear systems
I am interested in the iterative solution (preferably Krylov-type solvers) of a problem $\boldsymbol{A}x=b$, with $x,b\in\mathbb{C}^{n\times1}$ and $\boldsymbol{A}\in\mathbb{C}^{n\times n}$. $\...
- 141
2 votes
1 answer
356 views
Methods to improve the efficiency and the memory requirement of LU factorization for complex symmetric system matrix
I want to solve a linear set of equations (Ax=b) using LU decomposition. My "A" matrix is a complex matrix which is ...
- 33
0 votes
0 answers
69 views
Split of complex parts in weak form
I am working on a numerical model to simulate the acoustic and elastic wave propagation in frequency domain via the Finite Element Method. Basically, the problem is to solve the Helmholtz equation in ...
- 145
2 votes
1 answer
501 views
Reference for QR algorithm for complex matrix
I am trying to find out if the known QR algorithm to find the eigenvalues of a real matrix, which can be found in the book Fundamentals of Matrix Computations, can also be used for complex matrices ...
- 31
6 votes
3 answers
339 views
Fast evaluation functions given by straight-line programs
I have a simple but long function that takes a vector x[10], and outputs a vector y[100]. It is an automatically generated eval function for a multivariate polynomial, ie, there is only (complex) ...
- 139
7 votes
2 answers
196 views
Algebraic multigrid for complex valued matrices
Assume one uses the classical AMG with Ruge-Stuben coarsening and direct interpolation for solving real valued problems. How can this approach be recycled to also solve complex valued problems like ...
- 850
1 vote
1 answer
597 views
Computing real normal modes from complex eigenvectors
I'm trying to get the normal modes of a system of springs and dasphots using the basic dynamic equations for a linear, damped elastic structure: $ M \ddot{u}(t) + C \dot{u}(t) + K u(t) = f(t) $ to ...
- 173
6 votes
2 answers
1k views
Complex Eigenvalues using eig (Matlab)
I wanted to find and plot the eigenvalues of large (around $1000\times1000$) matrices. But discovered when using the eig function in matlab, it gives complex ...
- 61