Algorithms for Finding Inverse of Two Patterned Matrices over

Algorithm 2

Finding inversion in for factorization of unknown.

Inverse2

{Calculates the inverse of in

(1)  if    then

(2) let   which satiefy in ;

(3)   return  ;

(4) else if  ,    then

(5)   return “ is not invertible”;

(6) else if   fails let satisfy ;

(7) let    GetFactors ;

(8)   if  , then

(9)     Inverse2   ;

(10)     Inverse2   ;

(11)    calculate using Chinese remaindering (Lemma 5);

(12)   else

(13)     Inverse2   ;

(14)    calculate using Newton-Hensel lifting (Lemma 6);

(15)   endif

(16)   return  ;

(17) endif

GetFactors  

(18) let  ;

(19) if (  then

(20)   return  ;

(21) endif

(22) let  ;

(23) let  ;

(24) if   then

(25)   return  ;

(26) endif

(27) let  ;

(28) return  ;