Why is it important to keep a symmetric positive definite, Basic Computer Science

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Why is it important to keep a symmetric positive definite

1. Why is it important to keep a symmetric positive definite iteration matrix Bk while seeking a minimum of a smooth function φ(x)? Does Newton's method automatically guarantee this?

2. Define descent direction and line search, and explain their relationship.

3. What is a gradient descent method? State two advantages and two disadvantages that it has over Newton's method for unconstrained optimization

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Basic Computer Science: Why is it important to keep a symmetric positive definite

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Basic Computer Science: Why is it important to keep a symmetric positive definite

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