# Questions tagged [complex]

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### optimization for complex number

I don't know how to solve the optimization problem. Please suggest a theory or approach to solving the above optimization problem.
128 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 ...
41 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 ...
205 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 ...
87 views

### Finding curves where function goes to zero in two dimensions

Suppose $f(x,y)$ is a complex function of two real arguments with roots* that are not discrete points but lie in curves. (Is there are term for this characteristic?) An example is shown below: the ...
267 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) ...
123 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 ...
134 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 ...
792 views

### Complex Eigenvalues using eig (Matlab)

I wanted to find and plot the eigenvalues of large matrices (around1000x1000). But discovered when using the eig function in matlab, it gives complex eigenvalues when it shouldn't. For example, in the ...
1k views

### Power of complex-valued neural network

I often see neural networks extended to complex-values. Those networks allow complex input, complex parameters, and complex output. My understanding is that the inner products and point nonlinearities ...
116 views

### Mapping from n x n complex symmetric tridiagonal to 2n x 2n real symmetric tridiagonal

In my program I have a complex symmetric tridiagonal matrix. In order to perform some algorithmic optimizations I am searching for a (ideally linear) mapping from $n\times n$ complex symmetric ...
96 views

### Numerical computation of the complex elliptic integral $E(k)$ for medium $|k|$

I have implemented Carlson's algorithm for $E(k)$ from Numerical computation of real or complex elliptic integrals (available from ArXiv eprint, see also DLMF). It is essentially his formula (46) ...
136 views

### What is the computational cost of using complex numbers in contrast to real numbers in matrix operations, e.g. $LU$ or $LDL^T$ factorizations? [duplicate]

I am curious about how much one loses in terms of computational cost when complex numbers are used instead of real numbers? I guess the number of floating-point operations and memory doubles, but I ...
398 views

### Arpack and Matlab give different values for eigenvalues

I am solving a generalized eigenvalues problem with inversed complex shift: $$(M-\sigma J)^{-1}J \boldsymbol{x} = \boldsymbol{x} \nu \enspace .$$ My matrices are obtained from a finite element ...
593 views

### Danger of complex arithmetics in scientific computing

The complex inner product $\langle u,v\rangle$ has two different definitions decided by conventions: $\bar{u}^Tv$ or $u^T\bar{v}$. In BLAS, I found the routines cdotu, zdotu, and cdotc, zdotc. The ...
432 views

### Reference BLAS/LAPACK from NETLIB is twice as fast as MKL for complex numbers

I'm solving the Helmholtz equation using PETSc. I found with the PETSc configure option --download-f-blas-lapack my program runs twice as fast over running it with ...