Power series expansions for the probability distribution, mean value and variance functions of a geometric process with gamma interarrival times

2021 ◽  
Vol 388 ◽  
pp. 113287
Author(s):  
Mustafa Hilmi Pekalp ◽  
Halil Aydoğdu
Keyword(s):  
Probability Distribution ◽  
Power Series ◽  
Mean Value ◽  
Series Expansions ◽  
Geometric Process ◽  
Variance Functions ◽  
Power Series Expansions ◽  
Interarrival Times

scholarly journals Parallel Software to Offset the Cost of Higher Precision

2021 ◽  
Vol 40 (2) ◽  
pp. 59-64
Author(s):  
Jan Verschelde
Keyword(s):  
Power Series ◽  
Parallel Algorithms ◽  
Series Expansions ◽  
Use Case ◽  
Double Precision ◽  
Algebraic Space ◽  
Space Curves ◽  
Computational Overhead ◽  
Power Series Expansions ◽  
The Cost

Hardware double precision is often insufficient to solve large scientific problems accurately. Computing in higher precision defined by software causes significant computational overhead. The application of parallel algorithms compensates for this overhead. Newton's method to develop power series expansions of algebraic space curves is the use case for this application.

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