# Tagged Questions

Questions on numerical analysis/numerical methods; methods for approximately solving various problems that often do not admit exact solutions.

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### Determine Value of Constant for Iterative Convergence

The question I am trying to answer is stated as follows: The iteration $x_{n+1} = 2 - (1+c)x_n + cx_n^3$ will converge to $\alpha = 1$ for some values of $c$ (provided that $x_0$ is sufficiently ...
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### Please help: My MATLAB code for solving a 2D Schrödinger equation keep giving me weird output.

I've been trying to solve the following Schrödinger equation numerically, -(\frac{\partial^2}{\partial y^2} + \frac{\partial^2}{\partial z^2})\Psi + \frac{\sinh^2(y) + \sinh^2(z)}{(\...
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I need to solve the following third order (non-linear) ODE by numerical methods: $$\tag{1} h^{3} \dfrac{d^3 h}{d x^3} = h-1.$$ By assumption, the solution should approach $... 2answers 428 views ### Numerical root finding of function with unknown parameters I have a multivariate function of which I want to find one of (or all) its roots. However, besides the variables, it also depends on a bunch of parameters. Now I only want to find roots which are ... 9answers 264 views ### How do I prove that$\sqrt{20+\sqrt{20+\sqrt{20}}}-\sqrt{20-\sqrt{20-\sqrt{20}}} \approx 1$How do I prove that $$\sqrt{20+\sqrt{20+\sqrt{20}}}-\sqrt{20-\sqrt{20-\sqrt{20}}} \approx 1$$ without using the calculator? 1answer 443 views ### How to evaluate a condition number for a function of several variables? I'm trying to get the condition number of a multivariate function$f(a,b,c)$to see if it is stable. I am reading the information here. I know how to do it for a$1$-dimensional function. But for a ... 1answer 41 views ### Gradient descent with linear perturbation Given a convex, differentiable function$f$(from a Hilbert space to$\mathbb{R}$) with a minimum (say$x^*$), I know you can find$x^*$using gradient descent. Suppose now that you apply gradient ... 1answer 447 views ### Stochastic gradient descent for convex optimization What happens if a convex objective is optimized by stochastic gradient descent? Is a global solution achieved? 1answer 66 views ### A Variant of Gradient Descent Suppose I have some objective function$f(\beta)$which I would like to minimize for$\beta$. A standard gradient descent would be$\beta^{(t+1)}=\beta^{(t)}-\alpha \nabla f(\beta^{(t)})$, where$\...
In order to find the local minima of a scalar function $p(x), x\in \mathbb{R}^3$, I know we can use the gradient descent method: $$x_{k+1}=x_k-\alpha_k \nabla_xp(x)$$ where $\alpha_k$ is the step size ...