for the HP 15C
RI - Rational interpolaton

Rational interpolation is suitable for interpolating logarithmic or exponential relations of the data points
e.g. NTC thermistor characteristics than Lagrange interpolation, with its better accuracy and less computational complexity.
Input
Resources to be used
Output

Program list for the HP 15C

RI - Rev.1.10 Sep. 30 2011
0001-42,21,13  LBL C
0002-      36  ENTER
0003-      36  ENTER
0004-      36  ENTER
0005-   45  3  RCL 3
0006-      30  -
0007-   43 16  ABS
0008-      34  x<>y
0009-45,30, 1  RCL- 1
0010-   43 16  ABS
0011-      30  -
0012-43, 5, 1  CF 1
0013-43,30, 1  TEST 1   // x>0? 
0014-43, 4  1  SF 1
0015-      33  R↓
0016-45,30, 3  RCL- 3
0017-   45  2  RCL 2
0018-45,30, 1  RCL- 1
0019-      20  ×
0020-   45  5  RCL 5
0021-45,30, 6  RCL- 6
0022-      20  ×
0023-      34  x<>y
0024-45,30, 1  RCL- 1
0025-   45  2  RCL 2
0026-45,30, 3  RCL- 3
0027-      20  ×
0028-   45  5  RCL 5
0029-45,30  4  RCL- 4
0030-      20  ×
0031-43, 6, 1  F? 1
0032-      34  x<>y
0033-      10  ÷
0034-      34  x<>y
0035-   45  6  RCL 6
0036-   45  4  RCL 4
0037-43, 6, 1  F? 1
0038-      34  x<>y
0039-   43 33  R↑
0040-      20  ×
0041-   43 36  LSTx
0042-      33  R↓
0043-      30  -
0044-       1  1
0045-   43 33  R↑
0046-      30  -
0047-      10  ÷
0048-   43 32  RTN

Formulas used

Rational interpolation
rational interpolation

Examples

NoteInterpolation
Common logarithms
Reverse interpolation
Temperature V.S. Resistance characteristic of an NTC thermistor
Operation
2.8 STO 1
3.0 STO 2
3.2 STO 3
0.44715803 STO 4
0.47712125 STO 5
0.50514998 ST0 6
3.1 GSB C
12.478 STO 1
 8.068 STO 2
 5.353 STO 3
20 STO 4
30 STO 5
40 STO 6
10.000 GSB C
ri ntc
Results
Y: 3.100000000
X: 0.491365525
Y: 10.00000000 
X: 24.94306610 

SEE ALSO

Online calculator - Rational interpolation and Lagrange interpolation
RI - Rational interpolation program for the HP 42S
Ostrowski's method - a root-finding method

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