You have a large sparse matrix that is not symmetric positive definite. Which solver should you use to solve Ax = b efficiently?

hard📝 Application Q15 of 15

SciPy - Sparse Linear Algebra

You have a large sparse matrix that is not symmetric positive definite. Which solver should you use to solve Ax = b efficiently?

AUse <code>cg</code> because it is always faster.

BConvert matrix to dense and use direct solver.

CUse <code>gmres</code> because it works for general matrices.

DUse <code>cg</code> after transposing the matrix.

Step-by-Step Solution

Solution:

Step 1: Identify matrix properties
The matrix is large, sparse, and not symmetric positive definite, so cg is not suitable.
Step 2: Choose appropriate solver
gmres can handle general matrices efficiently without requiring symmetry or positive definiteness.
Step 3: Avoid dense conversion
Converting to dense wastes memory and time, so it is not efficient.
Final Answer:
Use gmres because it works for general matrices. -> Option C
Quick Check:
gmres handles general sparse matrices [OK]

Quick Trick: Use gmres for non-symmetric or indefinite sparse matrices [OK]

Common Mistakes:

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