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# Questions tagged [numerics]

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1 vote
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
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
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
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 $V(k,l)$ ...
40 views

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
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
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 ...
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 vote
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
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 $B$...
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
96 views

• 71
122 views

### Different Results for Double Pendulum

In this study, (Hidden Fractals in the Dynamics of the Compound Double Pendulum) the authors provide various fliptime fractals (of a double pendulum) for different length combinations. However, when I ...
• 121
I have a sparse, undirected and unweighted graph $G$ of size $n$, with $n$ on the order of say several million. I would like to compute the Fiedler vector $f$ of $G$, which is the eigenvector ...