The finitistic dimension conjecture says that the projective dimension of finitely generated modules over an Artin algebra is bounded when finite. The conjecture is known for algebras of representation dimension 3, for modules of Loevey length 2 and for stratifying systems with at most 2 indecomposable modules of infinite projective dimension (Huard, Lanzilotta, Mendoza [4]). We would like to i...

It is ~hown in this paper that a theoretical method of centers, introduced by Huard, converges linearly. It is also shown, by counter-example, that a modified me thod of centers due to I luard and a method of feas ible direction due to Topkis and Veino! canno t converge linearly even under convexity assumpt ions. Because of this, a new modified method of centers is introduced wh ich uses a quad...

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