CS 240A Lectures 4 5 Dense linear algebra

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CS 240A Lectures 4 - 5Dense linear algebra

• Lorin Hochstein on the HPCS workflow experiments
• Problems in dense linear algebra
• Matrix multiplication I cache issues
• Matrix multiplication II parallel issues
• Gaussian elimination
• Library software LAPACK, ScaLapack

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References

• Kathy Yelicks slides on matmul and cache
  issueshttp//www.cs.berkeley.edu/yelick/cs267/l
  ectures/03/lect03-matmul.ppt
• Kathy Yelicks slides on parallel matrix
  multiplicationhttp//www.cs.berkeley.edu/yelick
  /cs267/lectures/13/lect13-pmatmul.ppt
• Jim Demmels slides on parallel dense linear
  algebrahttp//www.cs.berkeley.edu/demmel/cs267_
  Spr99/Lectures/Lect_19_2000.ppt

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Problems in linear algebra

• Solving linear equations
• Find x such that Ax b
• Workhorse of computational modeling
• Dense electromagnetics kernel in sparse
• Sparse differential equations, etc. (later)
• Eigenvalue / eigenvector
• Find ? and x such that Ax ?x
• Dynamics of systems vibration information
  retrieval
• Matrix matrix multiplication
• Compute C A B
• Kernel in linear equation solvers, etc.