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https://github.com/brayvid/numerical-analysis

Algorithms from "Numerical Analysis" by Burden and Faires.
https://github.com/brayvid/numerical-analysis

differential-equations interpolation linear-algebra numerical-methods root-finding

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Algorithms from "Numerical Analysis" by Burden and Faires.

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# Numerical Analysis Algorithms

Matlab scripts and functions developed from theory presented in [Numerical Analysis 9e](https://www.amazon.com/Numerical-Analysis-Richard-L-Burden/dp/0538733519 "Numerical Analysis 9e at Amazon.com") by Burden, Faires.

```matlab
>> Examples
```

```console
Bisection method

ans =

10×2 table

n p_n
__ ______

1 1.5
2 1.25
3 1.125
4 1.1875
5 1.1562
6 1.1406
7 1.1484
8 1.1445
9 1.1465
10 1.1455

Fixed-point iteration

ans =

5×2 table

n pn
_ _______

1 0.532
2 0.57528
3 0.5952
4 0.60543
5 0.61096

Newton's method

ans =

5×2 table

n p_n
_ ______

0 1
1 1.2241
2 1.1943
3 1.1937
4 1.1937

Lagrange interpolation

ans =

0.0283165*x^3 - 0.31374*x^2 + 1.43615*x - 1.15073

Natural cubic spline interpolation

ans =

7.81781*x^3 + 9.38137*x^2 + 5.35154*x + 1.11375
- 7.81781*x^3 + 3.47526*x + 0.98867

Neville's interpolation

ans =

- 2.7*x^2 + 0.21*x + 0.85

Jacobi Iteration:

ans =

1.0000
2.0000
-1.0000
1.0000

Euler's Method

ans =

4×3 table

t y dydt
____ ______ ______

1 4 5
1.15 4.75 5
1.3 5.5196 5.1304
1.45 6.3064 5.2458

Runge-Kutta 4th order

ans =

11×3 table

t y dydt
____ ______ ______

1 2 2
1.04 2.0817 2.0851
1.08 2.167 2.1815
1.12 2.2564 2.2913
1.16 2.3505 2.4172
1.2 2.45 2.5625
1.24 2.5558 2.7313
1.28 2.6689 2.929
1.32 2.7906 3.1626
1.36 2.9225 3.4414
1.4 3.0667 3.7778
```