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

By Helmuth Späth, Werner Rheinboldt

This quantity offers an outline of numerical equipment for linear regression, together with FORTRAN subroutines. Linear regression has valuable purposes in company, facts and engineering and this paintings covers all 3 vital instances the place p=1,2 and infinity

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T h e p r o p o s e d i t e r a t i v e i m p r o v e m e n t of t h e s o l u t i o n i n [3,4] is i m p l e m e n t e d i n [21,22]. 4). I n t h i s c a s e , t h e n o r m a l e q u a t i o n s a r e simplified, a n d w e n o t e a n i m p o r t a n t f e a t u r e of t h e r e s i d u a l vector r . 4), w e will u s e /•(x) = JCo + { a , - ä , ) x , + . · . 6) i n t h e form of =h, (e, xo G fR, χ 6 fR^ w h e r e A is o b t a i n e d from A b y s u b t r a c t i n g t h e m e a n v a l u e % of t h e c o r r e s p o n d i n g c o l u m n from e a c h e l e m e n t of t h e kth c o l u m n .

C o m p u t a . BIO, 5 1 7 5 2 7 (1981). [14] Longley, J. W,: L e a s t S q u a r e s C o m p u t a t i o n s U s i n g O r t h o g o ­ n a l i z a t i o n M e t h o d s . M a r c e l D e k k e r , N e w Y o r k 1984. [15] Markah, T. , Plemmons, R. : C o n v e r g e n c e of a [16] [17] [18] [19] [20] [21] D i r e c t - I t e r a t i v e M e t h o d for L a r g e - S c a l e L e a s t - S q u a r e s P r o b l e m s . L i n . A l g . A p p l . 6 9 , 1 5 5 - 1 6 7 (1985). , Pillis, J. de. Varga, R.

EPS Quantity for the accuracy test for the orthogonalization. If the squared Euclidean length of the vector to be treated in the /eth step is smaller than EPS, then it is interrupted with IFLAG = 1. FALSE, the method is applied to (A, b) and χ is calculated. , X can easily be determined for another right-hand side Β (only the new Β is orthogonalized). IFLAG =0: No error was recognized. = 1: Error (see above). R ARRAY(NDIM, N)\ working area. Necessary subroutines: None. Remarks: Double precision is used for scalar products.

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