Fixed Point Iterations
Objective
 | Contraction mapping and Function iteration method
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Vocabulary
Functional iteration, Seidel method
Concepts
| Brouwer fixed point theorem (Review)
| Uniqueness of fixed point and derivative bounds
| Functional iteration and contraction mapping
| Theoretical and Computable (though often pessimistic) error bounds
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Method properties:
Extra:
| Choice of initial guess not obvious
| Often used as a brute force approach or method of last resort even if
derivative bounds are not satisfied
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Correction to Misconceptions
Fixed point iteration in higher dimension
Objective
| Contraction mapping and Function iteration method |
| Seidel's method to speed convergence |
Vocabulary
Functional iteration, Seidel method
Concepts
| Brouwer fixed point theorem (Review) |
| Uniqueness of fixed point and derivative bounds |
| Functional iteration and contraction mapping |
| Use of Seidel's method to accelerate convergence |
| Theoretical and Computable (though often pessimistic) error bounds |
Extra:
| Choice of initial guess not obvious |
| Often used as a brute force approach or method of last resort even if
derivative bounds are not satisfied |
Correction to Misconceptions
|