TY - GEN
T1 - Solving linear systems through nested dissection
AU - Alon, Noga
AU - Yuster, Raphael
PY - 2010
Y1 - 2010
N2 - The generalized nested dissection method, developed by Lipton, Rose, and Tarjan, is a seminal method for solving a linear system Ax = b where A is a symmetric positive definite matrix. The method runs extremely fast whenever A is a well-separable matrix (such as matrices whose underlying support is planar or avoids a fixed minor). In this work we extend the nested dissection method to apply to any nonsingular well-separable matrix over any field. The running times we obtain essentially match those of the nested dissection method.
AB - The generalized nested dissection method, developed by Lipton, Rose, and Tarjan, is a seminal method for solving a linear system Ax = b where A is a symmetric positive definite matrix. The method runs extremely fast whenever A is a well-separable matrix (such as matrices whose underlying support is planar or avoids a fixed minor). In this work we extend the nested dissection method to apply to any nonsingular well-separable matrix over any field. The running times we obtain essentially match those of the nested dissection method.
KW - Gaussian elimination
KW - Linear system
KW - Nested dissection
UR - https://www.scopus.com/pages/publications/78751562562
U2 - 10.1109/FOCS.2010.28
DO - 10.1109/FOCS.2010.28
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AN - SCOPUS:78751562562
SN - 9780769542447
T3 - Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS
SP - 225
EP - 234
BT - Proceedings - 2010 IEEE 51st Annual Symposium on Foundations of Computer Science, FOCS 2010
PB - IEEE Computer Society
T2 - 2010 IEEE 51st Annual Symposium on Foundations of Computer Science, FOCS 2010
Y2 - 23 October 2010 through 26 October 2010
ER -