Department of Mathematics: Difference between revisions
Created page with "Title: Department of Mathematics Research Question: The main research question of this paper is to analyze the complexity of the Simplex Method, a widely used algorithm for solving linear programming problems. The authors want to know if this method has polynomial smoothed complexity, which is a hybrid of the worst-case and average-case analysis of algorithms. Methodology: The authors introduce the concept of "smoothed analysis of algorithms," which measures the maximu..." |
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Title: Department of Mathematics | Title: Department of Mathematics | ||
Research Question: | Research Question: How can the complexity of curve fitting algorithms be reduced while maintaining accuracy? | ||
Methodology: The authors | Methodology: The study focuses on a popular algorithm for fitting polynomial curves to scattered data based on the least squares with gradient weights. The authors propose precise conditions under which this algorithm can be significantly simplified. | ||
Results: The authors | Results: The research reveals that this reduction in complexity is possible when fitting circles but not ellipses or hyperbolas. The authors introduce the concept of a gradient weight function, which is crucial for maintaining accuracy. They also provide insights into how to evaluate the distance from a point to the curve, making the algorithm more efficient. | ||
Implications: | Implications: The findings have significant implications for the field of curve fitting. The proposed method allows for a substantial reduction in computational complexity without compromising accuracy. This can lead to faster and more efficient algorithms, particularly useful for large datasets. Moreover, the research provides a clear understanding of the conditions under which such reductions are possible, which can guide future research in this area. | ||
Link to Article: https://arxiv.org/abs/ | Link to Article: https://arxiv.org/abs/0308023v1 | ||
Authors: | Authors: | ||
arXiv ID: | arXiv ID: 0308023v1 | ||
[[Category:Computer Science]] | [[Category:Computer Science]] | ||
[[Category: | [[Category:Research]] | ||
[[Category:Can]] | |||
[[Category:Fitting]] | |||
[[Category:Which]] | [[Category:Which]] | ||
[[Category: | [[Category:This]] | ||
Latest revision as of 14:07, 24 December 2023
Title: Department of Mathematics
Research Question: How can the complexity of curve fitting algorithms be reduced while maintaining accuracy?
Methodology: The study focuses on a popular algorithm for fitting polynomial curves to scattered data based on the least squares with gradient weights. The authors propose precise conditions under which this algorithm can be significantly simplified.
Results: The research reveals that this reduction in complexity is possible when fitting circles but not ellipses or hyperbolas. The authors introduce the concept of a gradient weight function, which is crucial for maintaining accuracy. They also provide insights into how to evaluate the distance from a point to the curve, making the algorithm more efficient.
Implications: The findings have significant implications for the field of curve fitting. The proposed method allows for a substantial reduction in computational complexity without compromising accuracy. This can lead to faster and more efficient algorithms, particularly useful for large datasets. Moreover, the research provides a clear understanding of the conditions under which such reductions are possible, which can guide future research in this area.
Link to Article: https://arxiv.org/abs/0308023v1 Authors: arXiv ID: 0308023v1