Given a sparse matrix A with 1 million rows and 10 million nonzero entries, which method is most efficient to solve Ax = b in SciPy?

hard📝 Application Q8 of 15

SciPy - Sparse Matrices (scipy.sparse)

Given a sparse matrix A with 1 million rows and 10 million nonzero entries, which method is most efficient to solve Ax = b in SciPy?

AUse iterative solvers like <code>cg</code> or <code>gmres</code> from <code>scipy.sparse.linalg</code>

BConvert <code>A</code> to dense and use <code>numpy.linalg.solve</code>

CUse <code>spsolve</code> directly on the dense matrix

DManually implement Gaussian elimination

Step-by-Step Solution

Solution:

Step 1: Consider matrix size
A is very large and sparse, so dense methods are infeasible due to memory.
Step 2: Choose solver type
Iterative solvers like cg (Conjugate Gradient) or gmres are designed for large sparse systems and scale better.
Final Answer:
Use iterative solvers like cg or gmres from scipy.sparse.linalg -> Option A
Quick Check:
Is dense conversion feasible? No. Use iterative methods. [OK]

Quick Trick: Use iterative solvers for very large sparse systems [OK]

Common Mistakes:

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