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ACM 48 2 Linear Lp Regression [22] Wampler, R. K: A l g o r i t h m 5 4 4 : L 2 A a n d L 2 B , W e i g h t e d L e a s t S q u a r e s S o l u t i o n s of Modified G r a m - S c h m i d t w i t h I t e r a t i v e R e f i n e m e n t . A C M T r a n s . M a t h . Softw. 5, 4 9 4 - 4 9 9 (1979). : N u m e r i c a l E x p e r i e n c e s w i t h a BlockR e l a x a t i o n M e t h o d for S o l v i n g L i n e a r L e a s t S q u a r e P r o b l e m s . C S Q 2 , 7 5 - 8 4 (1986). , Rijk, P. P. M.
14) is decomposed i n t o mxo = e^B, A^Ax = A^B. DZERO L O G I C A L BNEW c c c c c O R T H O G O N A L I Z A T I O N ( R ( K , K ) W I L L C O N T A I N THE R E C I P R O C A L V A L U E S OF THE SQUARED LENGTHS OF THE ORTHOGONAL V E C T O R S . WITH D = 1 . / D I A G ( R ) WE HAVE A * * T * A = R * * T * D * R , WHERE NOW D I A G ( R ) = I ) . c 10 20 IFLAG^O SZERO=0. DZERO^^O. /SSUM R{K,K)=H SUM^DZERO DO 3 0 1 = 1 , Μ SUM=SUM+DBLE(A(I,K))*DBLE(B(I)) CONTINUE SSUM=SUM SSUM=SSUM*R(K,K) X(K)=SSUM I F ( K .
106534E^02 0. 728072E-»00 0. 150935E+01 0, 127990E + 03 0 . 398362Ε+01 - . 3 7 3 3 1 2 E + 0 0 0. 3 1 4 6 8 6 E + 01 0 . 4 0 1 0 8 3 Ε + 01 0 . 8 5 9 5 0 7 E 4 0 1 0. 143509E + 02 -. 550358E^00 . 1 4 0 5 9 6 E + 01 0. 990707E 02 0 . lOOOOOE+01 0 . 285671E 02 - . 6 8 5 3 6 1 E - 0 2 0. 199720E+01 0 . 2 9 9 3 9 9 E + 0 1 - . 3 9 9 0 1 6 E + 01 0 . lOOOOOE+01 0 . 128001E+01 0 . lOOOOOE^Ol 0 . 235848E-06 0 . 199999E+01 0. 375000E+01 - . OOOOOOE+00 0 . 1 5 0 0 0 0 E l O l SEC Figure 5. Results of MGS.