Numerical Analysis: Difference between revisions
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Define the Homotopy map<br> | Define the Homotopy map<br> | ||
<math>H(x, \lambda)=\lambda r(x) + (1-\lambda)(x-a)</math> | <math>H(x, \lambda)=\lambda r(x) + (1-\lambda)(x-a)</math> | ||
==Numerical Differentiation== | |||
See finite differencing | |||
==Numerical Integration== | |||
See Quadrature rules | |||
Revision as of 20:23, 31 January 2020
Numerical Analysis
Orthogonal Polynomials
Hermite Polynomials
Legendre Polynomials
Laguerre Polynomials
Nonlinear Equations
Continuation/Homotopy Methods
Reference Numerical Optimization by Nocedal and Wright (2006)
Also known as zero-path following.
If you want to solve \(\displaystyle r(x)=0\) when \(\displaystyle r(x)\) is difficult (i.e. has non-singular Jacobian) then you can use this method.
Define the Homotopy map
\(\displaystyle H(x, \lambda)=\lambda r(x) + (1-\lambda)(x-a)\)
Numerical Differentiation
See finite differencing
Numerical Integration
See Quadrature rules