MAT 4725 Numerical Analysis Section 7.3 Iterative Techniques

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Presentation transcript:

MAT 4725 Numerical Analysis Section 7.3 Iterative Techniques

Maple Testing computer numbers 01v, 02v, 06v, 07vx, 11x, 12v, 16v and 17v.

Homework Induction – P(1) Basic algebraic proofs See me ….

Preview Focus on theoretical issues Jacobi Iterative Method

The need of iterative methods

Finding inverse… o Extremely expensive (time and storage) o More or less o Difficult/Impossible to implement in real time

Chapter 7 Iterative Techniques in Matrix Algebra Section 2.2 Fixed-Point Iteration

Chapter 7 Iterative Techniques in Matrix Algebra Section 7.3 Iterative Techniques

Section 2.2 Example 1 Show that if p is a fixed point of then p is a solution of

Idea

Example 1

Jacobi Iterative Method

Jacobi Iterative Method: Matrix Form

Convergence

Lemma c.f.

Theorem

HW

Corollary HW

Section 2.2 Corollary 2.4

Homework Download HW Read 8.2