Polynóm (mnohočlen) je súčet alebo rozdiel jednočlenov - poznatok z Wikipédie, bez výčitiek sa priamo priznám že toto nie je moja parketa.

Našiel som basic-ový program, takže nech je vidieť čo sa kedysi na "starečkovi" vtedy dalo vypočítať (popis výpočtu je v programe v riadkoch 9000 ÷ 9070):

10 FOR I=1 TO 16:PRINT:NEXT:PRINT "BEST FIT POLYNOMIAL"
20 PRINT"-------------------":PRINT:GOTO 9000
30 DIM X(50),Y(50),B(19),A(10,11),Z(19)
40 INPUT "NO. OF POINTS";N:FOR I=1 TO N
50 PRINT "X("I")=";:INPUT X(I)
60 PRINT,"Y("I")=";:INPUT Y(I):NEXT I
65 INPUT "DEGREE OF POLYNOMIAL";N1
70 N2=N1+1:N3=2*N1+1:N4=N2+1
80 FOR I=1 TO N3:Z(I)=0:IF I<=N2 THEN A(I,N4)=0
90 NEXT I
100 Z(1)=N:B(1)=1:FOR I=1 TO N
110 A(1,N4)=A(1,N4)+Y(I):FOR J=2 TO N3
120 B(J)=X(I)*B(J-1):Z(J)=Z(J)+B(J)
130 IF J<=N2 THEN A(J,N4)=A(J,N4)+B(J)*Y(I)
140 NEXT J:NEXT I
150 FOR I=1 TO N2:FOR J=1 TO N2
160 A(I,J)=Z(I+J-1):NEXT J:NEXT I
5100 FOR K=1 TO N2:P=A(K,K):A(K,K)=1
5110 IF P=0 THEN PRINT "ZERO DIAG ELEMENT":END
5120 FOR J=K+1 TO N4:A(K,J)=A(K,J)/P:NEXT J:I=1
5130 IF I=K THEN 5200
5140 R=A(I,K):FOR J=1 TO N4
5150 A(I,J)=A(I,J)-R*A(K,J):NEXT J
5160 A(I,K)=0
5200 I=I+1:IF I=N4 THEN 5250
5210 GOTO 5130
5250 NEXT K:PRINT "COEFFS ARE:-"
5260 FOR I=1 TO N2:PRINT "X("I")="A(I,N4)
5270 NEXT:C2=0:INPUT "TABLE NEEDED";Q$
5280 IF LEFT$(Q$,1)="Y" THEN PRINT "X-DATA","Y-DATA","Y CALCULATED"
5282 FOR I=1 TO N:Y2=A(1,N4):FOR J=2 TO N2
5290 IF X(I)<>0 THEN Y2=Y2+A(J,N4)*X(I)^(J-1)
5300 NEXT J:Y1=Y(I)-Y2:C2=C2+Y1*Y1
5305 IF LEFT$(Q$,1)="Y" THEN PRINT X(I),Y(I),Y2:NEXT
5310 IF N=N2 THEN 5330
5320 C2=C2/(N-N2)
5330 PRINT "CHI=";SQR(ABS(C2)):END
9000 PRINT "THIS PROGRAM FITS A POLYNOMIAL OF ANY"
9010 PRINT "DEGREE TO A SET OF DATA OF Y AND X"
9020 PRINT "THE POLYNOMIAL IS:"
9030 PRINT "Y=X(1)+X(2)*X+X(3)*X^2+...+X(N+1)*X^N"
9040 PRINT "THE PROGRAM WILL ALSO PRINT A TABLE OF"
9050 PRINT "THE DATA COMPARED TO CALCULATED RESULTS"
9060 PRINT "AND THE VALUE OF 'CHI': A MEASURE OF 'FITNESS'"
9070 PRINT "(CHI IS SMALLER FOR A BETTER FIT)"
9080 GOTO 30

Download programu:

Polynom.txt (1,73 kb)

P.S.:

Koho zaujímajú výpočty - pozrite si túto knihu kde sú ďalšie matematické programy (mimo iného):

https://archive.org/details/very-important-programs-for-ohio-scientific

Funguje pre SBC6502, Ohio Superboard a UK101.

Ukážka zoznamu matematických výpočtov z tejto knihy:

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