Using Cholesky decomposition and sparse matrices for conditional simulation of a gaussian 2D random field
Other Title(s)
استخدام تحليل تشولسكي و المصفوفات شبه الفارغة لإجراء محاكاة مشروطة لحقل عشوائي ثنائي يتبع غاوص
Author
Source
Damascus University Journal of Engineering Sciences
Issue
Vol. 33, Issue 1 (30 Jun. 2017), pp.17-30, 14 p.
Publisher
Publication Date
2017-06-30
Country of Publication
Syria
No. of Pages
14
Main Subjects
Abstract EN
This study presents an efficient practical method for the generation of sequential conditional simulation of a Gaussian two-dimensional random field which we frequently encounter in GIS spatial analysis problems such as DEM’s generation from a limited number of data.
The many realizations typically correspond to many reasons such as the geospatial uncertainty, the morphological perturbations over the surface having a complex structure or the inadequate representation of the triangulated network TIN or grid.
These realizations with simulation-based concept enable the performance and uncertainty assessment that tunes to various geospatial (GIS) applications.
For DEM generation and implementation of the conditional simulation, we need to decompose the covariance matrix of the data points and grid nodes by Cholesky Decomposition.
Conditional simulation respect data values and transfers those values into the grid nodes.
With the Incomplete Cholesky decomposition of the covariance matrix, we can produces as many simulations as needed in a single step with an accuracy, in a global sense, much better than the Moving Window Kriging method.
In other words, we don’t need to repeat covariance matrix generation and decomposition many times.
On the other hand, there is the problem of producing covariance matrices in the case of large dataset, which proved to be time consuming and may take several hours on PC.
The present paper presents a solution to this problem using Sparse Matrices Technique and Cholesky decomposition to achieve conditional simulation, reducing the time required for computations dramatically, as well as decreasing the demand of large amount of computer memory.
For the purpose of this study and testing all algorithms, a MATLAB Programs were made by the author.
They have been used in all computation stages and applied using real data.
The study has shown that we can reduce computation time by 85%-95% according to the scale of the problem yet saving a considerable space in memory needed to store matrices.
American Psychological Association (APA)
al-Abd Allah, Muhammad Salih. 2017. Using Cholesky decomposition and sparse matrices for conditional simulation of a gaussian 2D random field. Damascus University Journal of Engineering Sciences،Vol. 33, no. 1, pp.17-30.
https://search.emarefa.net/detail/BIM-873963
Modern Language Association (MLA)
al-Abd Allah, Muhammad Salih. Using Cholesky decomposition and sparse matrices for conditional simulation of a gaussian 2D random field. Damascus University Journal of Engineering Sciences Vol. 33, no. 1 (2017), pp.17-30.
https://search.emarefa.net/detail/BIM-873963
American Medical Association (AMA)
al-Abd Allah, Muhammad Salih. Using Cholesky decomposition and sparse matrices for conditional simulation of a gaussian 2D random field. Damascus University Journal of Engineering Sciences. 2017. Vol. 33, no. 1, pp.17-30.
https://search.emarefa.net/detail/BIM-873963
Data Type
Journal Articles
Language
English
Notes
Includes appendices : p. 25-28
Record ID
BIM-873963