Quasi-Newton Methods
Objective
 | Broyden’s method as an efficient way to apply concept from Newton’s
method
| Efficient computation of inverse of a matrix with a rank-1 update |
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Vocabulary
Rank 1 update, Sherman-Morrison formula
Concepts
| Entries in Jacobian matrix may be approximated by finite differences
| Deteriotion of rate of convergence from quadratic to superlinear
| Initial computation of inverse requires O(n3) operations using
Gauss Elimination
| Sherman-Morrison implies subsequent calculation requires O(n2)
operations
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Extra:
| Hessian |
Correction to Misconceptions
| Broyden’s method is implemented by explicitly calculating the inverse
using Sherman Morrison formula. Gauss elimination is used only for
constructing the inverse of the initial (exact or approximate) Jacobian
matrix.
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