[NA] 수치해석 관련 쿼리

[원쿼리맨]

근사공식(Taylor series)을 이용해서 지수 e의 값을 구해본다.
(exp(1)의 값과 비교해 보자.)




SELECT EXP (1) exp_1, SUM (nth) OVER (ORDER BY ROWNUM) exponential
  FROM (SELECT     EXP (SUM (LN (1 / GREATEST (LEVEL - 1, 1))) OVER (ORDER BY LEVEL)
                       ) nth
              FROM DUAL
        CONNECT BY LEVEL <= 35)



좌측 컬럼이 exp(1)의 값이고, 우측 컬럼이 근사값을 계산한 것이다.
34차 근사(34번째 미분항)까지 구해본다.





                                   EXP_1                              EXPONENTIAL
---------------------------------------- ----------------------------------------
2.71828182845904523536028747135266249776                                        1
2.71828182845904523536028747135266249776                                        2
2.71828182845904523536028747135266249776                                      2.5
2.71828182845904523536028747135266249776 2.66666666666666666666666666666666666666
2.71828182845904523536028747135266249776 2.70833333333333333333333333333333333333
2.71828182845904523536028747135266249776 2.71666666666666666666666666666666666666
2.71828182845904523536028747135266249776 2.71805555555555555555555555555555555555
2.71828182845904523536028747135266249776 2.71825396825396825396825396825396825396
2.71828182845904523536028747135266249776 2.71827876984126984126984126984126984126
2.71828182845904523536028747135266249776 2.71828152557319223985890652557319223985
2.71828182845904523536028747135266249776 2.71828180114638447971781305114638447971
2.71828182845904523536028747135266249776 2.71828182619849286515953182619849286515
2.71828182845904523536028747135266249776 2.71828182828616856394634172411950189727
2.71828182845904523536028747135266249776 2.71828182844675900231455787011342566897
2.71828182845904523536028747135266249776 2.71828182845822974791228759482727736695
2.71828182845904523536028747135266249776 2.71828182845899446428546957647486748015
2.71828182845904523536028747135266249776 2.71828182845904225905879345032784186222
2.71828182845904523536028747135266249776 2.71828182845904507051604779584860506117
2.71828182845904523536028747135266249776 2.71828182845904522670811748171086968333
2.71828182845904523536028747135266249776 2.71828182845904523492875272833519940029
2.71828182845904523536028747135266249776 2.71828182845904523533978449066641588614
2.71828182845904523536028747135266249776 2.71828182845904523535935743172980714737
2.71828182845904523536028747135266249776  2.7182818284590452353602471108690522047
2.71828182845904523536028747135266249776 2.71828182845904523536028579257075851154
2.71828182845904523536028747135266249776 2.71828182845904523536028740430832960766
2.71828182845904523536028747135266249776  2.7182818284590452353602874687778324515
2.71828182845904523536028747135266249776 2.71828182845904523536028747125742871472
2.71828182845904523536028747135266249776 2.71828182845904523536028747134926561336
2.71828182845904523536028747135266249776  2.7182818284590452353602874713525455026
2.71828182845904523536028747135266249776 2.71828182845904523536028747135265860223
2.71828182845904523536028747135266249776 2.71828182845904523536028747135266237222
2.71828182845904523536028747135266249776 2.71828182845904523536028747135266249383
2.71828182845904523536028747135266249776 2.71828182845904523536028747135266249763
2.71828182845904523536028747135266249776 2.71828182845904523536028747135266249775
2.71828182845904523536028747135266249776 2.71828182845904523536028747135266249775