Download Mathematical Algorithms for Linear Regression by Helmuth Späth, Werner Rheinboldt PDF

By Helmuth Späth, Werner Rheinboldt

This quantity provides an summary of numerical equipment for linear regression, together with FORTRAN subroutines. Linear regression has beneficial functions in enterprise, facts and engineering and this paintings covers all 3 vital instances the place p=1,2 and infinity

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Example text

4. I n F i g . 5, w h e r e t h e r e s u l t s of M G S for a l l 4 2 e x a m p l e s a r e g i v e n , M G S g i v e s t h e d e s i r e d s o l u t i o n χ = y ( l , 1,1)^ for E x a m p l e 30. «S m e a n s t h e v a l u e II A x - B | | 2 for t h e s o l u t i o n v e c t o r x , c a l c u l a t e d w i t h d o u b l e preci­ sion. T h e o t h e r n o t a t i o n s i n F i g . 5 a r e s e l f - e x p l a n a t o r y . S i m i l a r p r o g r a m s c a n b e found i n [ 1 , 5 , 1 3 , 1 4 ] .

E - 9 a n d E P S = l . E - 1 2 ) ; t h e o t h e r s u b r o u t i n e s give 8 i d e n t i c a l d e c i m a l p l a c e s for S a n d 6 for x . The computing times were measured by t h e available subroutine G E T T I M , w h i c h w a s a c t i v a t e d i m m e d i a t e l y before a n d after c a l l i n g u p t h e p r e c e d i n g s u b r o u t i n e s . A n e r r o r i n m e a s u r e m e n t of 5 t o 1 0 % is possible. F o r N G L , M G S , G I V R , a n d H F T I t h e c o m p u t i n g t i m e s m e a s u r e d i n t h i s w a y for a l l 4 2 e x a m p l e s t o g e t h e r a r e g i v e n i n t h e first c o l u m n of F i g .

We have Ö"kRANK+1 = υ V F * · - ^η^^' ARRAY(MDIM, Ν) ^ ARRAY(MDIM, Ν) i working areas. ARRAYiN) ) Remark: The working areas U and V do not agree with the matrices of the same name in the singular value decomposition. Necessary subroutines: SVD [6]. Remark: This subroutine should only be used if rank(A) < τι is suspected, or if cond2(A) is to be estimated. A and Β will not be destroyed. ) Figure 13. Program description for SVDR. h o l d . 22) m e a n s t h a t t h e difference of t h e r e s i d u a l s of t h e o r i g i n a l a n d t h e d i s t u r b e d p r o b l e m r e l a t i v e t o t h e size of b is b o u n d e d a b o v e b y t h e r e l a t i v e e r r o r of t h e c h a n g e s i n Λ a n d b m u l t i p l i e d b y C O N D .

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