which Solvers are efficient?

ImanJoon · November 12, 2010, 09:00

May explain that "TDMA algorithm" is efficient yet or not?
which new solvers are there for solving equations system?

walli · November 12, 2010, 13:16

You should make your question more precise. Which algorithm is efficient often depends on the structure and properties of your system of equations. Why TDMA is efficient is more or less obvious... For tridiagonal matrices, the Gaussian elimination can be done in O(n) instead of O(n^3) due to the tridiagonal pattern. Unfortunately, tridiagonal matrices are not very common in real applications. Typically, only simple one-dimensional problems can be formulated as a tridiagonal system.

lava12005 · November 13, 2010, 06:31

Well for the case of TDMA, it's actually just a backward substitution. So I think for the case of tridiagonal matrix TDMA is most efficient solver.

ztdep · November 19, 2010, 07:37

TDMA can be used only when the matrix have five diagonals
if you obtaned the matrix on a unstructed grid system, krylov iteration method is strongly sugguested.
Regards

November 12, 2010, 09:00	which Solvers are efficient?	#1
ImanJoon New Member Iman Harimi Join Date: Nov 2010 Location: Iran Posts: 1 Rep Power: 0	May explain that "TDMA algorithm" is efficient yet or not? which new solvers are there for solving equations system?

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November 12, 2010, 13:16		#2
walli New Member Join Date: May 2009 Posts: 28 Rep Power: 17	You should make your question more precise. Which algorithm is efficient often depends on the structure and properties of your system of equations. Why TDMA is efficient is more or less obvious... For tridiagonal matrices, the Gaussian elimination can be done in O(n) instead of O(n^3) due to the tridiagonal pattern. Unfortunately, tridiagonal matrices are not very common in real applications. Typically, only simple one-dimensional problems can be formulated as a tridiagonal system.

November 13, 2010, 06:31		#3
lava12005 Senior Member KHB Join Date: Aug 2010 Location: Singapore Posts: 118 Rep Power: 16	Well for the case of TDMA, it's actually just a backward substitution. So I think for the case of tridiagonal matrix TDMA is most efficient solver.

November 19, 2010, 07:37		#4
ztdep Senior Member p ding Join Date: Mar 2009 Posts: 427 Rep Power: 19	TDMA can be used only when the matrix have five diagonals if you obtaned the matrix on a unstructed grid system, krylov iteration method is strongly sugguested. Regards