scholarly journals Solving Linear Systems through Nested Dissection

2010 ◽  
Author(s):  
Noga Alon ◽  
Raphael Yuster
Keyword(s):  
Linear Systems ◽  
Nested Dissection

scholarly journals Global Astrometric Solutions with Sparse Matrix Techniques

2000 ◽  
Vol 180 ◽  
pp. 127-131
Author(s):  
Richard L. Branham
Keyword(s):  
Linear Systems ◽  
Sparse Matrix ◽  
Nested Dissection ◽  
Numerical Experimentation ◽  
The Matrix ◽  
Hall Property ◽  
Sparse Matrix Techniques ◽  
Dynamic Data Structure ◽  
Large Linear Systems ◽  
Dynamic Hashing

AbstractModern astrometric techniques lead to large, linear systems solved by the precepts of least-squares. These systems are usually sparse, and one should take advantage of the sparsity to facilitate their solution. As long as the matrix A of the equations of condition possesses the weak Hall property, characteristic of linear systems derived from astrometric reductions, it is possible to find a sparse Cholesky factor. Before the equations of condition are accumulated, by use of the fast Givens transformation, a symbolic factorization of A using Tewarson’s length of intersection technique determines the ordering of the columns of A that result in low fill-in. The non-null elements are stored in a sparse, dynamic data structure by use of dynamic hashing. Numerical experimentation shows that this competes well with alternatives such as nested dissection, and large, but sparse, linear systems with several thousand unknowns can be solved in a reasonable amount of time, even on personal computers.

A COMINRES-QLP Method for Solving Complex Symmetric Linear Systems

2020 ◽  
Vol 140 (12) ◽  
pp. 832-841
Author(s):  
Lijun Liu ◽  
Kazuaki Sekiya ◽  
Masao Ogino ◽  
Koki Masui
Keyword(s):  
Linear Systems ◽  
Complex Symmetric Linear Systems ◽  
Complex Symmetric
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