wowo0709

wowo0709

큰 사람이 되려면 큰 물에서 놀아라

[NumericalAnalysis] Nonlinear Systems 1

less than 1 minute read


Root Finding

Root Finding Problem

image-20211118112308125


Characterizing Problems

image-20211118112337241

image-20211118112408453



Bisection

Intermediate Value Theorem

image-20211118112505454


Reasonable Input

image-20211118112527198


Bisection

image-20211118112614826


Two Important Questions

image-20211118112635655


Conclusion

image-20211118112654006



Fixed Point Iteration

Fixed Points

image-20211118112726260


Convergence Criterion

image-20211118112752851


Graphical Illustration

image-20211118112818562


Example

image-20211118112837330



Newton’s Method

Differentiability Assumption

image-20211118112928575


Newton’s Method

image-20211118112954126


Convergence of Newton

image-20211118113017327


Graphical Illustration

image-20211118113039122


Example

image-20211118113056781



Secant Method

Secant Method

image-20211118113131932


Convergence Rate

image-20211118113152901


Graphical Illustration

image-20211118113214415


Example

image-20211118113231552



Dekker’s Method

Hybrid Methods

image-20211118113305845


Dekker’s Method

image-20211118113336044



Single-Variable Conclusion

image-20211118113357528



Leave a comment

You may also enjoy