Questions tagged [numerics]
The numerics tag has no usage guidance.
76
questions
1
vote
0
answers
36
views
Understanding this code to truncate the SVD
In Brunton's and Kutz's data-driven science and engineering book, page $19$, is a description of one way to truncate the SVD of a given matrix
I want to understand what the code for the variable <...
- 111
0
votes
1
answer
39
views
Estimating the rate of convergence of Projected Gradient Descent on constrained polynomial objectives
I am estimating the order of convergence of Projected Gradient Descent (GD) on quadratic polynomials with random coefficients independently drawn from Uniform(-1,1) and bounded by a unit hypercube. I'...
- 23
3
votes
0
answers
118
views
Quantifying the inefficiency of Gauss–Hermite quadrature
I am trying to understand the following part of the paper https://doi.org/10.1137/20M1389522 where the author argues about the inefficiency of Gauss-Hermite quadrature.
I think I get the gist of the ...
- 31
0
votes
0
answers
36
views
Solving for expectation using iteration in a implicit function
For a implicit function $V(k,l)$, taking $l$ as given and $k$ to be the only variable, $k$ is sampling from an unknown distribution and $\mathbb{E}k = \bar{K}$. Using Taylor expansion on $V(k,l)$ ...
- 55
0
votes
0
answers
40
views
Advanced computing on FPGA
I am an absolute beginner in the FPGA topic (so far I have only implemented a couple of simple logic gates in Verilog and simulated them in ModelSim). I studied digital electronics, logic elements, ...
- 131
1
vote
0
answers
33
views
Imposing higher order finite difference schemes for boundary value problems on a finite interval
I have some questions. I'm going to assume everything is in 1d with a Laplacian operator. If I discretize the Laplacian operator using $p = 2a+1$ grid points with periodic boundary conditions, I ...
- 111
0
votes
0
answers
57
views
On Newton-Raphson Method for Single Degree of Freedom Systems
I am trying to understand the geometric interpretation of the Newton-Raphson method as used in nonlinear structural mechanics. The fundamental governing equation of nonlinear structural mechanics is ...
0
votes
0
answers
49
views
How to solve the heat equation using the spectral method (Chebyshev's differentiation matrix), with constant flux boundary condition on both sides?
I am trying to solve a 1d heat equation with a constant flux boundary condition on the right-hand side and a zero flux boundary condition on the left-hand side. I've gained a lot of insight from ...
- 1
1
vote
1
answer
117
views
On the calculation of the first m generalized eigenvectors
This is a classic generalized eigenvalue/eigenvector problem:
$$
A\,\vec{x}=\lambda\,B\,\vec{x}
$$
which, however, is characterized by:
$A,B$ are real, symmetric and positive definite matrices of ...
- 113
5
votes
2
answers
156
views
Optimized Lanczos method for finding eigenvalues of $A \otimes B$
Recently my supervisor told me about an efficient way to calculate eigenvalues and eigenvectors of matrix $A \otimes B$ with $a_{1} \times a_{2}$ as dimensions of $A$ and $b_{1} \times b_{2}$ is of $B$...
4
votes
3
answers
642
views
Analysis of convergence of Newton method
I often used the Newton-Raphson method in material calculation, where I had to solve a small set of nonlinear equations (size=1..5). In most cases, it worked. However, convergence failure is often ...
- 289
1
vote
0
answers
96
views
Implicit-Explicit Operator Splitting Scheme
I am trying to solve the 2D advection-diffusion equation in cylindrical coordinates:
$$
\frac{\partial c}{\partial t} = D\left(\frac{\partial^2 c}{\partial r^2} + \frac{1}{r}\frac{\partial c}{\partial ...
- 11
6
votes
2
answers
376
views
Order of numerical solver when calculating difference between forwards and backwards solution
I'm working in applied oceanography, where people are sometimes interested in calculating ``backwards trajectories'' of things floating on the ocean, i.e., going backwards in time to figure out where ...
- 243
1
vote
0
answers
120
views
Iterative PDE solver for 1D Burgers equation
I am looking for an Iterative Numerical PDE solver for 1D Burgers equation. I need to have access to the intermediate solutions of the Numerical Solver. By iterative methods, I mean techniques which ...
- 11
1
vote
2
answers
124
views
Monotonicity of Errors with Respect to Step Sizes in Numerical Methods for PDEs
Consider a non-linear partial differential equation (PDE) (e.g., Burgers' equation) that is solved numerically using a finite difference method (or a similar approach). Suppose a grid search is ...
- 169