IEEE trans. on comput.

Abstracts of c.a.d, literature Mathematical techniques Beltraml, E J a n d Indusi, J P 73 1 'An a d a p t i v e r a n d o m search a l g o r i t h m for c o n s t r a i n e d m l m m l z a t l o n ' I E E E Tran~ on C o m p u t , Vol C-21 ( S e p t e m b e r 1972) No 9, pp 1 0 0 4 - - 1 0 0 8 Fhe a u t h o r s i n t r o d u c e r e f i n e m e n t s i n t o the r a n d o m i z e d p a t t e r n search m e t h o d The r a n d o m i z e d m e t h o d of L a w r e n c e and Stelghtz a u g m e n t s the a b i l i t y o f the m e t h o d to a d a p t to d i r e c t i o n A n a l g o r i t h m is derived t h a t m a k e s t h e m e t h o d m o r e adaptive in step size and i n c o r p o r a t e s p e n a l t v t e r m s to a c c o m m o d a t e c o n s t r a i n t s The a l g o r i t h m is r o b u s t and rehable and offers a s c h e m e for o b t a i n i n g b a l l - p a r k e s t i m a t e s o f a constrained global minimum Fletcher, R 73 2 ' F o r t r a n s u b r o u t i n e s for m i n i m i z a t i o n by q u a s i - N e w t o n m e t h o d s ' A t o m i c E n e r g y Res Est , Harwell, E n g l a n d ( J u n e 1 9 7 2 ) 31 pp Two q u a s i - N e w t o n s u b r o u t i n e s are p r e s e n t e d for m i n i m i z i n g a f u n c t i o n F ( x ) of n variables x The g r a d i e n t v e c t o r and the Hessian m a t r i x are a s s u m e d t o e x i s t

G u p t a , A K a n d Mohraz, B 73 3 'A m e t h o d of c o m p u t i n g n u m e r i c a l l y Integrated stiffness m a t r i c e s ' l n t J f o r N u m e r Ical M e t b o d s tn E n g , V o 1 1 5 ( A u g u s t S e p t e m b e r 1 9 7 2 ) No 1, pp 8 3 - 8 9 The a u t h o r s use i n d e x n o t a t i o n to achieve better organization and consequently obtain s u b s t a n t i a l r e d u c t i o n s in the c o m p u t a t i o n s for i n t e g r a t i n g a n d e v a l u a t i n g t h e e l e m e n t stiffness m a t r i x Hyslop, J 73 4 'A n o t e on the a c c u r a c y of o p t i m i z a t i o n technlqu6s' C o m p u t J , Vol 15 (May 1972) No 2, p 140 The a c c u r a c y of l o c a t i n g a s t a t i o n a r y value of a f u n c t i o n using d i r e c t search t e c h n i q u e s , is c o n s i d e r a b l y less t h a n the c o r r e s p o n d i n g precision t h a t can be a t t a i n e d b y d e t e r m i n i n g the actual m a g n i t u d e of the s t a t i o n a r y value Mayama, K 73 5 ' A p r o c e d u r e to d e t e r m i n e m t e r s e c t m n s b e t w e e n p o l y h e d r a l o b j e c t s ' I n t J o] C o m p u t and InJ Scz , Vot 1 ( S e p t e m b e r 1972) No 3, pp 2 5 5 - 2 6 6 Face-to-lace i n t e r s e c t i o n analysis is used to d e t e r m i n e w h e t h e r t w o or m o r e p o l y h e d r a l objects i n t e r s e c t A s o l u t i o n b o x a p p r o a c h is c o n s i d e r e d t o g e t h e r w i t h m u t u a l divisibility and v i s i b i l i t y o f t w o faces as a m e a n s ot m i n i m i z i n g the n u m b e r of pairs of faces to be e x a m i n e d Parity m o d e d e t e r m i n a t i o n is used to d e t e c t the i n t e r s e c t i o n b e t w e e n the t w o faces McCormick, G P 73 6 ' A l g o r i t h m i c and c o m p u t a t i o n a l a s p e c t s o f the use of o p t i m i z a t i o n m e t h o d s in engineering design' George W a s h i n g t o n University, School ot Eng and A p p l i e d Science, USA (19 pp, 19 ref)

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Pavelko, V L , Fadeev, V V a n d T~skova, A G 73 7 'An a l g o r i t h m and a p r o g r a m for c h o o s i n g an a p p r o x i m a t i n g e q u a t i o n w i t h the m a x i m u m degree of c o r r e l a t i o n ' Moscove, N a n c Ibled l n s t A e r o k h m , T Vvp 77 ( 1 9 7 1 ) pp 52--55 (refs in Russian) Schultz, M H 73 8 'Discrete F c h e b y c h e f f a p p r o x i m a t i o n for m u l t i v a r i a t e sphnes' l o,¢ C o m p and S y s S c I , Vol 6 ( A u g u s t 1972) No 4, pp 2 9 8 - 3 0 4 A t h e o r e t i c a l analysis for the c o m b i n a t i o n of two ideas In n u m e r i c a l analysis The first, an a p p r o x i m a t i o n of T c h e b y c h e f f ' s a p p r o x i m a tion to a f u n c t i o n over a c o n t i n u u m , X, b~ a p p r o x i m a t i o n s over finite d i s c r e t e subsets of k" The second, is the use of m u l n v a r l a t e spllne f u n c t i o n s as a p p r o x l m a t o r s Su, S Y H a n d C h e u n g , P T 73 9 ' C o m p u t e r m i n i m i z a t i o n of m u l t i v a l u e d s w i t c h i n g f u n c t i o n s ' I E F F Trans on C o m p u t , Vol C-21 ( S e p t e m b e r 1972) No 9, pp 9 9 5 - 1003 Multi-valued s w i t c h i n g t u n c t l o n s are repres e n t e d bv an array of cubes, a f o r m c o n v e n i e n t t o t p r o c e s s i n g b y digital c o m p u t e r The cubical r e p r e s e n t a t i o n has a d v a n t a g e s over a map, e q u a t i o n or t o p o l o g i c a l r e p r e s e n t a t i o n The cubical n o t a t i o n i n t r o d u c e d is seen as a p o w e r f u l tool for m i n i m i z i n g m u l t i - v a l u e d s w i t c h i n g f u n c t i o n s and can be e x t e n d e d to m u l t i p l e - o u t p u t m u l t i - v a l u e d s w i t c h i n g funct i o n s b y a d d i n g m o r e c o l u m n s The algorlthrns d e s c r i b e d have been p r o g r a m m e d in Fortran

Graphical techniques Aklma, H 73 10 ' I n t e r p o l a t i o n and s m o o t h curve f i t t i n g based on local p r o c e d u r e s ( A l g o r i t h m 4 3 3 ) ' C o m m u n A C M , Vol 15 ( O c t o b e r 1972) No 10, pp 9 1 4 - - 9 1 8 Details and listing are given of an a l g o r i t h m w r i t t e n an F o r t r a n for s m o o t h i n g curves There are two s u b r o u t i n e s listed, I N T R P L , w h i c h p e r f o r m s the i n t e r p o l a t i o n , and C R V F I T w h i c h fits a s m o o t h curve to a given set o f I n p u t data p o i n t s in an xzv plane Pfaltz, J L 73 11 'Graph Structures' J oJ the 4C~1, Vol 19 ( J u l y 1972) No 3, pp 4 1 0 - 4 2 2 The paper d e v e l o p s the c o n c e p t ot a graph s t r u c t u r e in ~h~ch a tree-hke assemblage of subgraphs is used t o r e p r e s e n t a d i r e c t e d graph Greenleaf, J F , Rltman, E L., Coulam, C M , Sturm, R . E and W o o d , E H 73 12 ' C o m p u t e r graphic t e c h n i q u e s tor s t u d y of t e m p o r a l and spatial r e l a t i o n s h i p s of m u l t i d i m e n s i o n a l d a t a derived f r o m biplane roentgen v l d e o g r a m s w i t h p a r t i c u l a r reference to cardio a n g i o g r a p h y ' C o m p u t and Btom e d w a l R e s , Vol 5 ( A u g u s t 1972) No 4, pp 3 6 8 - 387 A c o m p u t e r - a u t o m a t e d biplane r o e n t g e n

v t d e o m e t c r has been d e v c l n p c d t . r d~ ia in t~ m e a s u r e m e n t ot the shape of the l i f t tvn trlcle Fhe paper de%rlbes the tombm.ttt¢ [1 of c o m p u t e r i z e d vldeometr~, w i t h ~o,,1 p u t e n z e d o s c i l l o s c o p i c and television scan converter d i s p l a y s and p r e s e n t s e x a m p l e s (~1 the resulting m u l t i d i m e n s i o n a l ,hspl )~ tormats H o r o w i t z , J and Hullender, W ( , ~ I ' C o m p u t e r graphics and scale m o d e l s (/,, m b n g P~ogre~s V o 1 6 8 (June 1972) No 6 pp 4 5 - 5 1 Leutt, K N a n d K a u t z , W H 7 • 14 Cellular a r r a y s i o r the s o l u t i o n ol graph p r o b l e m s ' C o m m A C~,1 Vot 15 ( S e p t e m b e r 1972) No 9 p p 7 8 9 - - 8 0 1 The p a p e r shows t h a t cellular a r r a ~ , ai~ i n h e r e n t l y s u i t e d for the s o l u t i o n o1 nlanX graph p r o b l e m s A cellular array conslst~ ot t w o - d i m e n s i o n a l c h e c k e r b o a r d tx pe m o d u l e s , t a c h Identical Several parallellzed a l g o r i t h m s are p r e s e n t e d to solve certain s p a n n i n g tre~ distance, and p a t h p r o b l e m s These hav~ direct a p p h c a t l o n s to wire r o u t e i n g aim th~ analvsls o1~ m a n y tvp~s o1 n e t w o r k s Pao, Y C 7~ 15 '& general p r o g r a m for c o m p u t e r p l o t t i n g ol Mohr's circle' C a m p u t and ~,t) t . t Vol 2 (.September 1972) No 4, pp 6 2 5 - - 0 3 5 The p a p e r describes, and Includes the hstlng of, a p r o g r a m for p l o t t i n g a t w o - d i m e n s i o n a l Mohr's circle The p r o g r a m can be a d a p t e d as a t e a c h i n g aid for m e c h a n l t s c o u r t s anti can be e m p l o y e d for engineering anal~ sis m practical design ot s t r u c t u r a l and m a d l t n t elements Purdom, P W and Moore, le 1~ 7~ it, ' I m m e d l a t c p r e d o m i n a t o r s in a dlreete,t g r a p h ' C o m m u n 4 C M Vol 15 (August 1972) No 8, pp 7 7 7 - 7 7 8 A F o r t r a n p r o c e d u r e called PRb I ) O M I N A FOR is described provMlng an a l g o r i t h m tot directed graphs

Rosenfeld, A,Lee, Y H 7g 17 'A c l u s t e r i n g heuristic for line-drawing analysis' I E F I ~ Trans (,~ ( o n ; p u t \ o l ( -21 ( A u g u s t 1972) No 8, pp 9 0 4 - - 9 1 1 A r r a n g e m e n t s ot local f e a t u r e s m .I . ~ ne often t e n d to group t o g e t h e r to be set n t. u n i t s Fhe a u t h o r s suggest t h a t m som~ ~ a ~ . the p h e n o m e n o n may be l n t t r p r c t e d t. process of cluster d e t e c t i o n in a graph s t r u c t u r e d space The idea 1~ Illustrate,] b~ c o n s i d e r i n g a class ot hne-drawlng sccne~ t h a t c o n t a i n onlx h o r i z o n t a l and vertical hqt s e g m e n t s A l t e r n a t i v e s to the descrlbt d m e t h o d of d e t l n m g the graphs of ltnL d~a~ lngs are c o n s i d e r e d

Cartography Bress, D L -~ l b ' C o m p u t e r s and ~artograph~ i ,,input .~ I 4utom Vol 21 ( A u g u s t 1972) No 8 pp 25 26

COMPU I E R A I I ) L I ) DI SI(,N