WP 34S Owner‘s Manual
Edition 2.2
Page 100 of 103
Name
Purpose and remarks
18 0.865063366688984510732096688423493
Location of g1, g8, k3 and k17
19 0.149451349150580593145776339657697
Gauss weight for g1 and g8
20 0.075039674810919952767043140916190
Kronrod weight for k3 and k17
21 0.679409568299024406234327365114874
Location of g2, g7, k5 and k15
22 0.219086362515982043995534934228163
Gauss weight for g2 and g7
23 0.109387158802297641899210590325805
Kronrod weight for k5 and k15
24 0.433395394129247190799265943165784
Location of g3, g6, k7 and k13
25 0.269266719309996355091226921569469
Gauss weight for g3 and g6
26 0.134709217311473325928054001771707
Kronrod weight for k7 and k13
27 0.148874338981631210884826001129720
Location of g4, g5, k9 and k11
28 0.295524224714752870173892994651338
Gauss weight for g4 and g5
29 0.147739104901338491374841515972068
Kronrod weight for k9 and k11
Constants 2 .. 29 are for the 10 / 21 point Gauss-Kronrod quadrature used by the
internal integration command. Locations are in the range (0, 1) which is scaled to
match the interval of integration. The quadrature sums the weight times the function
value at each location to estimate the integral. In Gauss-Kronrod schemes the
Gauss points are common to both quadratures although the weights are different.
This means two estimates of the integral can be performed without increasing the
number of function evaluations which in turn allows an estimate of the error to be
made. The cost for this is a reduction in the degree of polynomial function that is
always integrated exactly.
The following two solver commands SLVI and SLVS may use some hidden regis-
ters and flags. The start points of the respective register and flag blocks are passed
as one argument
n
.
Registers:
n
+0 ,
n
+1: first two estimates
a
and
b
for the root
n
+2:
third estimate
c
n
+3:
function value at first estimate
f(
a
)
n
+4:
function value at second estimate
f(
b
)
Flags:
n
+0 ..
n
+7: an eight bit iteration counter
n
+8:
―bracket flag‖ – true if we've got an interval with
f(a)
*
f(b)
< 0
n
+9:
true if all function evaluations have been constant so far
SLVI
n
Initializes the solver. SLVI clears the iteration counter, takes
a
and
b
and calculates
f(
a
)
and
f(
b
)
, sets the last 2 flags accordingly, and produces a guess
c
. There is no
stack interaction.
SLVS
n
Solver step. Updates the internal solver state based on the last function evaluation.
In particular, SLVS takes
a
,
b
,
c
,
f(
a
)
, and
f(
b
)
from the register block plus
f(
c
)
from
X
and updates the register values so that
c
and
f(
c
)
replace one of
a
and
f(
a
)
or
b
and
f(
b
).
It also produces a new guess
c
and returns zero in
X
if the solving should
continue and non-zero if not. Otherwise, the stack isn't altered.
