Basic HTML version of Foils prepared 8 November 1995

Foil 34 Direct Solution Method for Ax=b

From Fox Presentation Fall 1995 CPS615 Basic Simulation Track for Computational Science -- Fall Semester 95. by Geoffrey C. Fox


Consider Ax = b solved "directly" which is Gaussian elimination where one succesively removes
  • x1 from Equation 2 to N,
  • x2 from Equations 3 to N etc.
Then this has memory requirement of order N2 and computational complexity of order N3
This is modified somewhat when you consider matrices A with a lot of zeroes and try hard to exploit these zeros i.e. avoid doing calculations which are irrelevant as adding or multiplying by zero
Of course this cannot be done by testing on matrix element being zero as modern computers do floating point arithmetic faster than or at least as fast as test!
Rather one arranges loops to not include zero elements -- if possible!



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