In this study, we focused on the interpolation methods for the
derivation of digital elevation models, based on field gridding
observations with different spacing.
In this paper, spline technique with five collocation parameters for finding the
numerical solutions of delay differential equations (DDEs) is introduced. The presented
method is based on the approximating the exact solution by C4-Hermite spline
i
nterpolation and as well as five collocation points at every subinterval of DDE.The study
shows that the spline solution of purposed technique is existent and unique and has
strongly stable for some collocation parameters. Moreover, this method if applied to test
problem will be consistent, p-stable and convergent from order nine .In addition ,it
possesses unbounded region of p-stability. Numerical experiments for four examples are
given to verify the reliability and efficiency of the purposed technique. Comparisons show
that numerical results of our method are more accurate than other methods.
We will first introduce the basic ingredient of Fourier methods in
section 1, then we will do some analysis on the Fourier
approximation, in the last section, we will apply the Fourier
method to solve some ODEs . we will write Matlab code for
num
erical result .
Compressive Sensing (CS) shows high promise for fully distributed
compression in wireless sensor networks (WSNs). In theory, CS
allows the approximation of the readings from a sensor field with
excellent accuracy, while collecting only a small fra
ction of them at
a data gathering point. However, the conditions under which CS
performs well are not necessarily met in practice. CS requires a
suitable transformation that makes the signal sparse in its domain.
Also, the transformation of the data given by the routing protocol
and network topology and the sparse representation of the signal
have to be incoherent, which is not straightforward to achieve in
real networks. In this paper we investigated the effectiveness of
data recovery through joint Compressive Sensing (CS) and
Principal Component Analysis (PCA) in actual WSN deployments.
We proposed a novel system, called CS-PCA that embeds a
feedback control mechanism to automatically change the
compression ratio through changing the number of transmitting
sensors, while bounding the reconstruction error. The considered
recovery techniques in the proposed system are: biharmonic Spline
(Spline), Deterministic Ordinary Least Square (DOLS),
Probabilistic Ordinary Least Square (POLS) and Joint CS and PCA
(CS-PCA). We found that the later outperform all other
interpolation technique in the case of slow varying signals, while
POLS was the most effective in case of fast varying signals that(
low correlation less than 0.45)
Groundwater is one of the major sources of exploitation in arid and semi-arid
regions, Thus for protecting groundwater quality, data on spatial and temporal distribution
are important. Geostatistics methods are one of the most advanced techniques f
or
interpolation of groundwater quality. In this research, IDW, Kriging methods were used for
predicting spatial distribution of nitrate NO3
-. Data were taken from 21 wells study within
eastern Damascus's Ghouta.
After normalization of data, variograme was drawn. The less RSS was used, so
Spherical model was the best. By using cross-validation and RMSE, the best method for
interpolation was selected; Results showed that Kriging method is superior to IDW
method.
there is a big spatial dependence for nitrate variable that amounts to 2.2 %. Finally,
maps of distribution of nitrate in groundwater were executed by Kriging method, in
addition to executed maps that show goodness of groundwater for drinking and irrigation.
Then it was prepared map of Probability Map of nitrate at threshold 50 mg/l.
In this paper, comparisons between several mathematical interpolation methods applied on high accuracy and huge laser clouds which only represents the DTM. In order to implicate the aforementioned, a group of a variety of Laser Scanned Areas has been
chosen to represent different types of terrain including complex and flat terrain, taking into account that man-made features are not involved in this study and that different Laser Clouds density is used to make the study more general.
A different set of algorithms were applied to conclude which one is more suitable. This step was followed by the comparison between different interpolation results. The results have shown that the Points'
Density has a great impact on a manner in which the optimal interpolation method is applied.
Moreover, it has proven that the Nearest Neighbor Algorithm is the best applied method compared with the other alternatives
Algorithm of fitting curves based on piecewise function composed of a set of
third degree polynomials is presented in this paper. These polynomials are
applicable to successive intervals of the given data points. This algorithm
applied to the meth
od of univariate interpolation, which developed by the
author [٦]. This method depends on the values of the first order derivative at
the data points.
