萌新求助，如何求一个未知表达式的多元函数的近似值 - mathematica吧

level 1

_Khattiya_ 楼主

有这么一个具体表达式未知的函数f(x,y)=(σ,θ)，可以用差分法算出一组函数值{[xn], [yn], [σn], [θn]}，但我想求得[xn], [yn]的区间内某个特定的(xi,yi)所对应近似解(σi,θi)（不需要求得拟合方程），用Fit试了一下好像解决不了我这种问题。。。
算例：
{(-10 - 9.3`- 8.6`- 7.899999999999999`- 7.1999999999999975`-
6.499999999999999` Null - (43/5) - 7.9`- 7.199999999999998`-
6.4999999999999964`- 5.799999999999999` Null Null - (36/5) -
6.5`- 5.799999999999997`-
5.099999999999997` Null Null Null - (29/5) - 5.1`-
4.4` Null Null Null Null - (22/5) -
3.6999999999999997` Null Null Null Null Null -
3), (7 8.077905474670207` 9.
15581094934
0417` 10.233716424010623` \
11.311621898680833` 12.389527373351038` Null 7 8.077905474670207` \
9.
15581094934
0413` 10.233716424010623` 11.311621898680828` Null Null \
7 8.077905474670207` 9.
15581094934
0413` 10.23371642401062` Null Null \
Null 7 8.077905474670207` 9.
15581094934
0417` Null Null Null Null 7 \
8.077905474670208` Null Null Null Null Null 7), (15/(1 +
Sin[24 \[Degree]]) 26.754129959808232` 42.845283253847164` \
58.93643654788603` 75.02758984192498` 91.1
18743135963
81` Null 15/(1 +
Sin[24 \[Degree]]) 26.754129959808232` 42.84528325384709` \
58.93643654788604` 75.02758984192485` Null Null 15/(1 +
Sin[24 \[Degree]]) 26.754129959808232` 42.8452832538471` \
58.93643654788595` Null Null Null 15/(1 +
Sin[24 \[Degree]]) 26.754129959808232` 42.845283253847164` Null \
Null Null Null 15/(1 +
Sin[24 \[Degree]]) 26.754129959808267` Null Null Null Null Null \
15/(1 + Sin[24 \[Degree]])), (\[Pi]/
2 1.5707963267948952` 1.5707963267948954` 1.5707963267948961` \
1.5707963267948966` 1.5707963267948966` Null \[Pi]/
2 1.5707963267948957` 1.5707963267948963` 1.5707963267948972` \
1.5707963267948966` Null Null \[Pi]/
2 1.570796326794896` 1.5707963267948972` 1.570796326794897` Null \
Null Null \[Pi]/
2 1.5707963267948963` 1.5707963267948963` Null Null Null Null \
\[Pi]/2 1.5707963267948968` Null Null Null Null Null \[Pi]/2)}

2022年06月18日 16点06分 1

level 1

_Khattiya_ 楼主

算例复制错了。。。
{{{-10, -9.3, -8.6, -7.9, -7.2, -6.5}, {Null, -(43/
5), -7.9, -7.2, -6.5, -5.8}, {Null,
Null, -(36/5), -6.5, -5.8, -5.1}, {Null, Null,
Null, -(29/5), -5.1, -4.4}, {Null, Null, Null,
Null, -(22/5), -3.7}, {Null, Null, Null, Null, Null, -3}}, {{7,
8.07791, 9.15581, 10.2337, 11.3116, 12.3895}, {Null, 7, 8.07791,
9.15581, 10.2337, 11.3116}, {Null, Null, 7, 8.07791, 9.15581,
10.2337}, {Null, Null, Null, 7, 8.07791, 9.15581}, {Null, Null,
Null, Null, 7, 8.07791}, {Null, Null, Null, Null, Null,
7}}, {{15/(1 + Sin[24 \[Degree]]), 26.7541, 42.8453, 58.9364,
75.0276, 91.1187}, {Null, 15/(1 + Sin[24 \[Degree]]), 26.7541,
42.8453, 58.9364, 75.0276}, {Null, Null,
15/(1 + Sin[24 \[Degree]]), 26.7541, 42.8453, 58.9364}, {Null,
Null, Null, 15/(1 + Sin[24 \[Degree]]), 26.7541, 42.8453}, {Null,
Null, Null, Null, 15/(1 + Sin[24 \[Degree]]), 26.7541}, {Null,
Null, Null, Null, Null, 15/(1 + Sin[24 \[Degree]])}}, {{\[Pi]/2,
1.5708, 1.5708, 1.5708, 1.5708, 1.5708}, {Null, \[Pi]/2, 1.5708,
1.5708, 1.5708, 1.5708}, {Null, Null, \[Pi]/2, 1.5708, 1.5708,
1.5708}, {Null, Null, Null, \[Pi]/2, 1.5708, 1.5708}, {Null, Null,
Null, Null, \[Pi]/2, 1.5708}, {Null, Null, Null, Null,
Null, \[Pi]/2}}}

2022年06月18日 16点06分 2