Information:
Large-scale finite element analysis (FEA) for structural engineering can produce linear systems with variables. Direct methods like Gaussian elimination require operations and memory. For dense storage in double precision (8 bytes per entry), an matrix needs bytes.
A company wants to solve a structural FEA problem with 1 million variables ( ) using Gaussian elimination. The system has 64 GB of RAM. Is Gaussian elimination feasible, and why?

Question

Information: 
 Large-scale finite element analysis (FEA) for structural engineering can produce linear systems with    variables. Direct methods like Gaussian elimination require    operations and    memory. For dense storage in double precision (8 bytes per entry), an    matrix needs    bytes. 
A company wants to solve a structural FEA problem with 1 million variables (  ) using Gaussian elimination. The system has 64 GB of RAM. Is Gaussian elimination feasible, and why?

Answer

No, because Gaussian elimination is numerically unstable for large

Answer

Yes, modern CPUs have enough cache to handle    matrices

Answer

Yes, Gaussian elimination is the fastest direct method and handles any size

Answer

No, because Gaussian elimination cannot process sparse matrices at all

Answer

Yes, partial pivoting reduces memory from    to    for large systems

Answer

No, dense storage needs    TB and    FLOPs would take years on one CPU

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