Texas Instruments TI-92+, Tip List

Page: 278 / 507

©Set Complex format to Rectangular
©
1 2may02/dburkett@infinet.com
local m,roots,eps,maxm,i,j,jj,ad,x,b,c,root
©------------------------------------------------------------
© Define local function to find
1 root with Laguerre'e method
Define root(a,x)=Func
©({coeffs},guess) polynomial root
©NOTE: {a} is reversed!
local m,maxit,mr,mt,epss,iter,j,abx,abp,abm,err,frac,dx,x 1 ,b,d,f,g,h,sq,gp,gm,g2
dim(a)- 1→ m © Find order of polynomial
2 ⁻1 2 → epss © Set estimated fractional error
8 → mr © Set number of fractional values to break limit cycles
1 0 → mt © Set number of steps to break limit cycle
mt*mr → maxit © Maximum number of iterations
{.5,.25,.75,. 1 3,.38,.62,.88, 1 .} → frac © Fractions used to break limit cycle
for iter, 1 ,maxit © Loop to find a root
a[m+ 1 ] → b
abs(b) → err
0 → d
0 → f
abs(x) → abx
for j,m, 1 , ⁻1 © Evaluate the polynomial and first two derivatives
x*f+d → f
x*d+b → d
x*b+a[j] → b
abs(b)+abx*err → err
endfor
epss*err
→ err © Estimate roundoff error in polynomial evaluation
if abs(b) ≤ err then © Return root if error condition met
return x
else
© Execute Laguerre's method
d/b → g
g^2 → g2
g2-2.*f/b → h
√ ((m- 1 )*(m*h-g2)) → sq
g+sq → gp
g-sq → gm
abs(gp) → abp
abs(gm) → abm
if abp < abm: gm → gp
if max(abp,abm)>0 then
m/gp
→ dx
else
ℯ ^(ln( 1 +abx)+iter*  ) → dx
endif
endif
x-dx
→ x 1
if x=x 1 :return x © Converged to root
if mod(iter,mt) ≠ 0 then © Every mt steps take a fractional step to break (rare) limit cycle
x 1→ x
else
x-dx*frac[iter/mt]
→ x
endif
endfor
return "polyroot too many its" © May have this error for complex roots
EndFunc
©-----------------------------------------------------------
© Begin polyroot()
dim(a)- 1→ m © Find order of polynomial
6 - 120