Rit (Vísindafélag Íslendinga) - 01.06.1946, Blaðsíða 31

31
Let the eqnation be:
c0 + cr\: + c2x2 +.....cmx"‘ =* 0 = y (57)
and by means of the assumption that (57) is an infinite series
where cr— 0 for r>m, an approximate determination of
the lowest root is then in many cases readiiy obtainable
from the equation:
°C 0 0 0 0 c{ c0 0 0 0
C2ci C00 0 c2 c, c0 0 0
C3 C2 Ci C0 0 -|- X C3 C2 C1 C0 0

r

r.
1
(58)
and similarly the numerical highest root is determined by:
Cm 0 0 0 ... 0 Cm —2 Cm —1 Cm 0...0 Cm —3 Cm—2 Cm —1 Cm' ' ' 0 Cm — 1 Cm 0 0 •••° Cm — 2 Cm — 1 Cm 0 • ■ • 0 Cm — 3 Cm —2 Cm-1 Cm- ‘" ®
X -f
.. c
m
.. c
* m—1
(58a)
If the equation (57) has no real root the formulas men-
tioned (58) and (58a) will not give any definite value for
x but oscillate as we go from lower r to higher one. Even in
some other cases the root found from (58) or (58a) may
turn out to be illusory if we use a rather small number for
r. It is therefore necessary to prove the result found, or
to solve also the quadratic equation resulting from s = 2