By P. Valko, S. Vajda

This ebook provides a realistic creation to numerical tools and provides easy subroutines for real-life computations within the components of chemistry, biology, and pharmacology. the alternative of easy because the programming language is inspired through its simplicity, its availability on all own desktops and by way of its strength in facts acquisition. whereas many of the medical programs at present to be had in uncomplicated date again to the interval of restricted reminiscence and pace, the subroutines provided the following can deal with a wide variety of life like issues of the ability and class wanted by means of execs and with easy, step by step directions for college students and newcomers. A diskette containing the 37 application modules and 39 pattern courses indexed within the booklet is accessible individually. the most activity thought of within the publication is that of extracting valuable details from measurements through modelling, simulation, and statistical facts reviews. effective and strong numerical equipment were selected to unravel comparable difficulties in numerical algebra, nonlinear equations and optimization, parameter estimation, sign processing, and differential equations.

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**Example text**

SOLUTlOli OF L I N E I R EOUMIONS U I T H TRIDIAGONBL #ATHI! I0 DRTA 5 11: DATA 4,2, =,I =,? 1! 01 RE! ---------- READ DATA :a2 HER3 I 104 D Ill A I1 ,B(N i,C(1; 1 ,D I 10 ,X ( k ! ,P (ti1 205 FOP I=! I0 HEAD B(I! 212 IF I < N THE# READ CiI) 214 HERD R$,O(I) 216 Rili 1 TIE REIl ---------- C K L SOLUTION MODULE 2 0 GOSUB 1780 2 2 :PRINT "SOLUTION:" :LPPINT 2 4 V$:STRING$i 15,"-" J 2 5 LF'RI#T " I X(I)n 228 LPHINT v1 2 3 FOE I:! 1 w e defined the eigenvalue h and the eigmvector u of the n m matrix A to satisfy the matrix equation (&XI)U = 0 .

A, . , . 4 Inversion of a square matrix by Gauss-Jordan elimination. To calculate the inverse of the matrix 5 3-1 0 2 0 4 1 A = -3 3 -3 5 0 4-2 3 consider the vectors a l , ~ , ~ , a 4 , e l and , ~ , e4, ~ where aj is the j-th colunn vector of A These coordinates are listed in the new DATA statements of the main program we used in the previous examples: . 188 RE\ 102 104 106 188 118 112 114 116 118 128 ________________________________________-------------------- REM EX. 4. INVERSION OF A IIATRIX BY GAUSS-JORDAN ELMINATION REM IIERGE Hl8 REM ---------- DATA REII (VECTOH DIHENSION, NUMBER OF VECTORS) DATA 4,8 DATA 5, 3,-1, 0, 1, 0, 0, 0 DATA 2, 8, 4, I , 8, 1, 0, 0 DATA -3, 3,-3, 5, 0, 0, 1, 0 DATA 0 , 6,-2, 3, 8, 8, 8, 1 REH ---------- FRDN HERE THE SAHE AS THE PROGRAH OF EX.

1 Solution of matrix equations We can use the LU decomposition to solve the equation clx = b very efficiently, where cl is a nonsingular square matrix. 45) P . 55) U x = d . 54). The next d u l e performs these . calculations Proqram rodule M15 On inplt the array FI contains the decomposed matrix as given by the module M14, and the right-hand side coefficients are placed into the vector X . (Ih wtput, this vector will store the solution. There is nothing to go wrong in backsubstitution if the previws decomposition was successful, and hence we dropped the error flag.