# Questions tagged [error-estimation]

The tag has no usage guidance.

134 questions
Filter by
Sorted by
Tagged with
1k views

### What does optimal convergence rate mean? How to prove whether a numerical method, e.g. FEM, has an optimal convergence rate or not?

I searched online about the way optimal is defined mathematically,but without any information acquired? How to prove whether a numerical method, e.g. FEM, has an optimal convergence rate or not? ...
373 views

### error estimator VS error indicator in the context of FEM error estimation

Is an error indicator an index for size measurement of something? And how is the relationship between the error estimator and error indicator? Is the error indicator just used for the (e.g. derivative)...
39 views

### Deterministic method to compute “Process noise covariance matrix, Q” for a Kalman filter when parameter variations of the model is known apriori

I am implementing a Kalman filter (for a linear ODE system for now). My model represents a physical device that has 6 "parameters", i.e. those values of the device do not evolve over time (within a ...
127 views

### Precision not improving by decreasing step-size in nonlinear Schrödinger

I tried to simulate soliton propagation by solving the nonlinear Schrödinger equation using the split-step Fourier method. The following is an example of the Matlab code copied from a textbook. ...
26 views

### How group similar data in a single classes and reduce the error

I have vehicles gps information in my real time traffic application. Averaging that information I know the speed of every road at any time. The problem is that is too much data to send back to the ...
49 views

### Quick evaluation of floating point Absolute Error

I need to to find a quick and dirty way to estimate the absolute error introduced by a series of agebraic operations of IEEE single precision floating point numbers, a pessimistic result is ok. The ...
71 views

### Dirichlet term in error estimations

I am working on a method based on moving least square approximation where shape functions do not satisfy Kroneker Delta property. So Dirichlet boundary condition should be enforced. I usually used ...
199 views

### Estimate $L_2$ norm of a elliptic problem with unknown exact solution on finite element method

I have the elliptic problem $$-\Delta u = 1,\,\,\Omega\subset\mathbb{R}^2$$ with $u=0$ on $\partial\Omega,$ with $\Omega=[-1,1]^2\backslash([0,1]\times[-1,0])$ and I want to estimate the $L_2$ error ...
106 views

### Relationship between global and local error?

In some cases I have seen that if the local error is: $Err = O (\Delta t^{p+1})$ where the global error is p. So if local error is 3, global will be 2. Does somebody know where it comes? For ...
383 views

### How can I derive the a priori error estimate for a symmetric bilinear form using lagrange finite elements?

Suppose that I'm solving the poisson equation by the finite element method by lagrange elements. I know that the error can be measured in a variety of ways, depending on which norm you choose. For a ...
517 views

### matlab lsqcurvefit parameter estimation journey

The lsqcurvefit solution in matlab converges at different solutions depending upon the initial guess: Surface represents the error (SSE) between model and data at various combinations of parameters ...
435 views

### $L^2$-error in FEM: how to compute integral over reference element?

I have the following problem. The domain is $(0,1)$ and we consider a uniform triangulation on $\hat{\Omega}$ with elements $K_i = [i/N,(i+1)/N]$ and $X_h^1$ the linear finite element space. I wrote ...
170 views

### How to optimally choose points for multivariable Hermite interpolation?

I have a multi-variate, continuous function $f$ from $R^n$ to $R$, which I can query for its output for any input. I would like to create interpolation polynomial for it. In one-dimensional case ...
7k views

### What is “tolerance” in ODE45 in Matlab?

I have used ode45 in Matlab. And, it is my understanding that the 4 and the 5 are for the order of the global and local error, respectively. So, the global error ...
227 views

### What is the error associated with Fornberg's algorithm?

Bengt Fornberg derived a general way to compute the weights for arbitrary finite difference schemes in two papers: his 1988 paper and (better) his 1998 paper. What are the numerical errors ...
87 views

I have solved a PDE with an analytical equation. Through operator splitting I divided the PDE into one PDE and one ODE, using a sequential approach. Finally for different $dt$, I got euclidian norm ...
56 views

### How can I compute the difference between shape function and dual solution in dwr?

I am trying to find error estimation based on weighted residual technique: $$Q(e_h)=\sum_{k \in {\cal T}}\eta_k,$$ where $$\eta_k=\int_kR(z-v_h)d\Omega+\int_{\partial k}J(z-v_h)ds,$$ or in the weak ...
134 views

### Stable computation of $\log\sum x_i$ from $\log x_i$, with many terms

Kahan's summation algorithm is a method to compute sums: $$\sum x_i$$ with many terms, without significant error. I want to do this with very large numbers, and instead of the numbers themselves, I ...
147 views

I am doing a nested integral via quadrature. To give a definite example, lets say: $$\int_0^2dx \left[x + \int_0^x dy \, 2y\right]$$ So effectively I'm integrating $x + x^2$ from 0 to 2 (although ...
54 views

104 views

### Using kalman filter when samples don't have time index

Assume $X$ and $N$ are two sets of observations from two different normal distribution, where $X$ represents clean data and $N$ represents noise; and $A$ a projection matrix of a filter and the ...
6k views

### Difference between l2 norm and L2 norm

What is the difference between the $l^2$ norm and the $L^2$ norm. I can not find a definitive reference. Wikipedia uses them interchangeably.
4k views

### How to avoid the round-off errors in the larger calculations?

Now I need to sum up more than one thousands of terms and then make the four-dimmensional integral in my Fortran program. I found that there are some numerical errors. Can you give me some suggestions ...
132 views

### Calculation of error

I have written a code in which I find the approximation of the solution of this elliptic problem. I calculated the error using the following part of code: http://pastebin.com/7b5mmuRW but I get the ...
2k views

### How can one describe the accuracy of a Runge-Kutta method?

I am solving a nonlinear ODE with a regular singularity using MATLAB ODE45 or ODE113. I am wondering what precision and accuracy they have and what one can say about the numerical error. The idea ...
467 views

### GSL linear algebra LU/determinant precision

I am working with symmetric matrices of order $n \times n$ where $n \leq 50$. The diagonal elements of my matrices are a fixed number $d$ and the off diagonal elements are limited to two small numbers ...
52 views

### problem about simulating recurrence relation

We have the recurrence relation: $5x_{n+1}-x_n=\frac{1}{3}$ $x_0=\frac{1}{12}$ solution: $y_h=(\frac{1}{5})^nC$ $y_p: 5A-A=\frac{1}{3}$ $A=\frac{1}{12}$ $y=(\frac{1}{5})^nC+\frac{1}{12}$ ...
159 views