# Tagged Questions

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### Get number equation using specific set of values for get given answer

I have do it for AI assignment. Need a logic for finding solution ..Here is the explanation of problem . I have answer ( any number like for example 10 ). And have some set of numbers (like for ...
42 views

### QR transformation with Householder transformation

It's a task i do to understand minimizing the error including the QR transformation with the help of Householder transformation. I think i really do something wrong but i dont get it running i hope ...
38 views

### How to characterise this non-linear optimisation (linear objective function, non-linear constraints)

I was wondering if someone may be able to help me characterise this optimisation problem as I am struggling to find a numerical library that will solve it and I suspect it is because I am using the ...
30 views

### Optimal numerial method for optimization of “Rosenbrock Banana”-like function

Which numerical methods would be optimal to find an extremum of a function with an almost flat "valley" (but a single minimum in the middle of the valley)? In this context optimal means the least ...
19 views

### Constraint approximation in non-linear optimization

In given non-linear optimization problem \begin{equation*} \begin{aligned} & \underset{x \in\mathbb R^n}{\text{maximize}} & & f(x) = \alpha^2 \\ & \text{subject to} & c(p(x)) \le ...
31 views

### Estimating rates of convergence

If I have a set of data points obtained from a numerical approximation say 15.3828 15.2458 15.2095 15.2003 how can I estimate the rate of convergence?
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### Simultaneous iteration of Symmetric Matrices

Given a Matrix $A$ we can use Simultaneous iteration(Using power iteration on all columns simultaneously) to compute the d biggest eigenvalues. Now this method will give you the biggest eigenvalues, ...
37 views

### Reference request: nonlinear systems, optimization, ode/pde

Could someone suggest me one or more good books on the following topics: Nonlinear systems: fixed point and Newton's method Optimization: steepest descent and Newton's-quasi newton methods ODE ...
29 views

### Hermite interpolation with interior points

I am trying to solve the following problem: Given the conditions on a curve c(u) of degree 4 at the points -1, 0, 1 as: c(-1) = 4; c'(-1) = 4; c(0) = 6; c(1) = -4; c'(1) = -6; find the generalized ...
126 views

### calculate Jacobian matrix without closed form or analytical form

The question is probably clear in the title. In many of my applications mostly computer vision, I might not have the closed-form or analytical form of f (a multivariable function). It's calculated ...
25 views

### Lowest norm solution to a system of polynomial equations

I have a system of cubic equations: $$0=A_0+A_1 x+A_2 ( x \otimes x ) + A_3( x \otimes x \otimes x )$$ where $\dim A_0 = \dim x$ (so there are as many equations as unknowns). You may assume that the ...
35 views

### Linear least squares with sparse inequality constraints for support function estimation

The initial problem is the following: $$||h - h^{0}|| \to min \; \; s.t. Qh \leq 0$$ where $h^{0} \in \mathbb{R}^{n}$ is known vector and $Q$ is a $m \times n$ matrix. The problem arises in specific ...
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### Can a 6-arm star be convex

Please help me with the following question. Suppose that the constant level contours of some function $V:\mathbb{R}^{2} \rightarrow \mathbb{R}$ have the shape of a symmetric 6-arm star. Can such a ...
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### Does a Convex Function need to be Continuous

I have been trying the following problem and I am very confused. If possible the problem should be solved with derivatives. If the derivative exists for all the points on the graph then it is ...
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### a conjugate gradients result for eigenvalue estimates

Consider the not preconditioned CG-method for a linear system $Ax=b$. Define $\beta_j = \frac{(r_{j+1},r_{j+1})}{(r_j,r_j)}$ and $\alpha_j=\frac{(r_j,r_j)}{(Ap_j,p_j)}$, where $(x,y) = y^Tx$ denotes ...
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### How to determine coefficients of $p(x) = x^6$ with the Chebyshev processing

I want to calculate the coefficients of $p(x) = x^6$ with the Chebyshev processing. How to do that? Following question would be, how to estimate the error in $[-1,1]$, if i only use terms until ...
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### Numerical Optimization methods?

What kind of functions are suitable for numerical optimization methods such as Newton, Gradient Descent, ... ? Any conditions?
140 views

### Speeding up the convergence for Steepest Descent Method

How would one speed up the convergence of the method of steepest descent when the minimum is in a very long, narrow structure? I know the fact that is a steep minimum covers more iterations to go ...
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### Better than Runge-Kutta-Fehlberg 4(5) at high order?

I wonder what are currently the best numerical solvers of ODE for high-accuracy computations. I need an efficient and accurate method to solve ODE that are not pathological (all is smooth) using ...
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Is there any example of a continuous differentiable function out there, in which the gradient method with Armijo's stepsize-rule doesn't converge? I found it pretty hard to create one myself because ...
127 views

### Qualities of Projected Gradient Methods

Consider the following constrained minimization problem: $min_{x \in X} \ f(x)$ where $X \subset \Bbb{R}^{n}$ is a nonempty closed convex set and f is continuously diferentiable. I'm ...
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### surface approximation using least squares

I am studying the following problem. Soppose you have two BeziÃ¨r patches with a common curve; suppose that the control points of the two patches are given by some initial guess (they are all known). ...
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### Formulate optimization problem

My research area has "nothing to do with mathematics" but I still find it full of optimization problems. Therefore, I would like to learn to formulate and solve such problems, even though I am not ...
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### Computation of gradient of FE-function

I have a vectorfield $f_h \in \mathbb{R}^3$, which is a Finite Element function, i.e. $f_h(x)= \sum_i f^i \phi_i$. Now, i want to compute $\nabla (I_h[f_h])$ on a triangulation, where $I_h$ is the ...
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### Maxima with equality constraints

I am trying to create an algorithm that finds the global maximum to a function with (in)equality constraints numerically. However, I am trying to fit that into a webpage (for example, via javascript. ...
307 views

### Finding a Fixed Point Solution

I'm trying to solve the following where $A,B >0$ in the most general case (don't assume they are equal). Wolfram Alpha cannot compute this in the allowed time, but I feel some fixed point ...
106 views

### Graphically, what is positive semidefinite-ness?

Suppose that we are trying to minimize a function $f$ on $\mathbb{R}^n$ and we apply Newton's method, updating: \begin{align} \mathbf{x}_{n+1} = \mathbf{x}_n - [\nabla^2 f(\mathbf{x}_n)]^{-1} \nabla ...
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### Numerical optimization question

I need to solve the following optimization problem. \begin{aligned} \min_{\lambda_0,\lambda_1} & \sum_{t=1}^T\sum_{n\in\{4,8,12,16\}} \left(\frac{1}{n}A_n + \frac{1}{n}B_n^\top X_t + ...
144 views

### Optimize material in a can

A can in the shape of a right circular cylinder is to be constructed to contain 1000 cm$^3$. The circular top and bottom of the can must have a radius of 0.25 cm more than the radius of the can so ...
I was recently working with functions of the form $$N - \sqrt{\frac{N}{x}}\cdot\left\lfloor \frac{N}{\sqrt{N/x}}\right\rfloor + \sqrt{\frac{N}{x}} - \left\lfloor \sqrt{\frac{N}{x}}\right\rfloor$$ ...