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AX + XB = C paper 2

AX + XB = C paper 2 - SUBROUTINE PIVOT N C P U R P O S E TO...

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SUBROUTINE PIVOT (N) C PURPOSE - TO PERFORM tHE PIVOI OPEIxATION BY UPDATING ]HE C INVERSE OF THE BASIS AND 0 VECTOR. C COMMON AM, O*LI,B, NLI,NL2,A*NEIsNE2, I~JMBASIS,~,Z DIMENSION AMCSO*SO), OCbO), BC50*50), ACbO) DIMENSION W(50)J Z(SO)* MBASIS(IOO) DO I I=I,N I B(IR, I)=B(IR*I)/A(IR) Q(IR)=Q(IR)/A(IR) D0 3 I=I~N IF {I.EO.IR} GO 70 3 Q(1):Q(1)-O(IR)*A(1) DO 2 J=I*N B(I~J)=B(I,J)-B(IR*J)*A(1) 0 CONTINUE 3 CONTINUE C UPDATE THE INDICATOR VECTOR OF BASIC VARIABLES NLI=MBASIS(IK) L=N+IR NL2=MBASIS(L) MBASISIIR)=NEI MBASIS(L)=NE2 LIfLI÷I RETURN END SUBROUTINE PPRINT (N) C PURPOSE - TO PRINT THE CURRENT SOLUTION TO COMPLEMENTARY C PROBLEM AND THE ITERATION NUMBER. O COMMON AM*OnLI,B*NLI*NL2,AsNEI*NE2*II(~MBASIS*~*Z DIMENSION AM(SO~bO)s O(SO)* B(50,5O)* A(50) DIMENSION ~(50}* Z(50)* NBASIS(IOO) ~RITE(6*I) LI 1 FORMAT (10X*I3RITERATION NO.~I4) I=N+I d=l 2 KI=MBASIS(1) KO=MBASIS(J) IF (O(J)*GE-O.O) GO TO 3 O(J)=O.O 3 IF (R2.EO.l) GO TO 5 WRITE(6~4) KI,O(J) A FORMAT (IOXt~HZ(JI4,2H)=JFI5°5) GO TO 7 5 WRITE(6*6' KI*Q(J) 6 FORMAT (IOXt2HW(~I4~OH)=~FISoS) 7 I=I+l J=J+l IF (J*LE.N) GO TO 2 RETURN END Editor's note: Algorithm 432 described here is available on magnetic tape from the Department of Computer Science, University of Colorado, Boulder, CO 80302. The cost for the tape is $16.00 (U.S. and Canada) or $18.00 (elsewhere). If the user sends a small tape (wt. less than 1 lb.) the algorithm will be copied on it and returned to him at a charge of $10.O0 ( U.S. only). All orders are to be prepaid with checks payable to ACM Algorithms. The algorithm is re corded as one file of BCD 80 character card images at 556 B.P.I., even parity, on seven ~rack tape. We will supply the algorithm at a density of 800 B.P.I. if requested. The cards for the algorithm are sequenced starting at 10 and incremented by 10. The sequence number is right justified in colums 80. Although we will make every attempt to insure that the algorithm conforms to the description printed here, we cannot guarantee it, nor can we guarantee that the algorithm is correct.--L.D.F. Algorithm 432 Solution of the Matrix Equation AX + XB = C [F4] R.H. Bartels and G.W. Stewart [Recd. 21 Oct. 1970 and 7 March 1971] Center for Numerical Analysis, The University of Texas at Austin, Austin, TX 78712 Key Words and Phrases: linear algebra, matrices, linear equa- tions CR Categories: 5.14 Language: Fortran Descdption The following programs are a collection of Fortran IV sub- routines to solve the matrix equation AX -.}- XB = C (1) where A, B, and C are real matrices of dimensions m X m, n X n, and m X n, respectively. Additional subroutines permit the efficient solution of the equation ArX + xa = C, (2) where C is symmetric. Equation (1) has applications to the direct solution of discrete Poisson equations [2]. It is well known that (1) has a unique solution if and only if the eigenvalues al , a2 .... , a,~ of A and ~l , ~2 , • . • , ~, of B satisfy ai + ~ # 0 (i = 1, 2, . . . , m;j = 1,2,...,11).
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