A new method of analysis of critical‐point singularities from power series expansions: Application to eigenvalue problems and virial series

1986 ◽  
Vol 85 (11) ◽  
pp. 6713-6719 ◽  
Author(s):  
Gustavo A. Arteca ◽  
Francisco M. Fernández ◽  
Eduardo A. Castro
Keyword(s):  
Power Series ◽  
Critical Point ◽  
Eigenvalue Problems ◽  
New Method ◽  
Series Expansions ◽  
Virial Series ◽  
Power Series Expansions

Method of analysis of critical-point singularities from power-series expansions

1986 ◽  
Vol 33 (2) ◽  
pp. 1297-1301 ◽  
Author(s):  
Gustavo A. Arteca ◽  
Francisco M. Fernández ◽  
Eduardo A. Castro
Keyword(s):  
Power Series ◽  
Critical Point ◽  
Series Expansions ◽  
Power Series Expansions

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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