CS267 - Lecture 3: Linear Algebra Optimization
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Questions and Answers

What was the world's record for matrix multiplication complexity in terms of big-O notation?

  • O(n^2.37548) (correct)
  • O(n^2.81)
  • O(n^2.37293)
  • O(n^2+ε)

    • Who achieved a new record for matrix multiplication complexity by reducing it from 2.37548 to 2.37293?

  • Alman and Williams
  • Jacob Scott
  • Coppersmith & Winograd
  • Virginia Vassilevska Williams (correct)

    • What did Lebeck mention as a possible extension for the communication lower bound?

  • Ω(n^2.81 / M^0.4) (correct)
  • Ω(n^2.37548)
  • Ω(n log^2 7 / M(log^2 7)/2 – 1)
  • Ω(n^2+ε)

    • Who suggested the possibility of an O(n^2+ε) algorithm?

    <p>Jacob Scott</p> Signup and view all the answers

    Which algorithm reduced the world's record of matrix multiplication complexity to 2.37286?

    <p>Alman and WIlliams</p> Signup and view all the answers

    What is the main focus of the given text?

    <p>Achieving optimal algorithms for array operations</p> Signup and view all the answers

    In the context of the text, what does 'Ax=b' refer to?

    <p>Solving a system of linear equations</p> Signup and view all the answers

    What is a key factor in determining the number of words moved according to the General Communication Lower Bound Thm?

    <p>The number of iterations in the program</p> Signup and view all the answers

    What type of linear program is used to minimize the value of sHBL in the General Communication Lower Bound Thm?

    <p>Linear programming</p> Signup and view all the answers

    What is the role of projections φj in determining the Communication Lower Bound Thm?

    <p>Calculating the number of words moved in memory</p> Signup and view all the answers

    Which recent mathematical result is crucial for proving the General Communication Lower Bound Thm?

    <p>'Hölder-Brascamp-Lieb (HBL)' inequality generalization</p> Signup and view all the answers

    What is the main focus of the lecture on 'Applications of Parallel Computing'?

    <p>Communication between main memory and cache</p> Signup and view all the answers

    In the context of communication lower bound, what is referred to as the most expensive operation?

    <p>Moving data between processors over a network</p> Signup and view all the answers

    For the n-body algorithm, what does the term 'array of structures' refer to?

    <p>An array representing the position and charge of particles</p> Signup and view all the answers

    In the context of n-body data access, what does 'access A(3), B(5)' imply?

    <p>Reading data entries from arrays A and B at indexes 3 and 5</p> Signup and view all the answers

    What is the maximum number of loop iterations that can be done if only 10 entries of A(i) and B(j) can be accessed?

    <p>25</p> Signup and view all the answers

    What is the purpose of optimizing tiling in the usual n-body algorithm?

    <p>To minimize data access patterns for improved performance</p> Signup and view all the answers

    'Optimal tiling (M=10)' in the usual n-body algorithm involves reading how many entries of A and B?

    <p>10 entries of A and 5 entries of B</p> Signup and view all the answers

    'C = A*B' in the context of linear algebra represents what operation?

    <p>'C' equals 'A' multiplied by 'B'</p> Signup and view all the answers

    'Communication Lower Bound on C = AꞏB' focuses on minimizing communication by limiting access to how many entries of A, B, and C in cache?

    <p>'M^2' entries each</p> Signup and view all the answers

    '# loop iterations doable with M words of data' is represented by which formula in the context of communication lower bound?

    <p>#cubes ≤ (M · M · M)^(1/2) = M^(3/2)</p> Signup and view all the answers

    What is the purpose of synchronization in parallel computing, as mentioned in the text?

    <p>To impose order constraints and protect shared data access</p> Signup and view all the answers

    In the context of parallel computing, what does the term 'critical region' refer to?

    <p>A section of code where thread synchronization is enforced</p> Signup and view all the answers

    What does the OpenMP directive 'barrier' primarily facilitate in parallel computing?

    <p>Ensuring that all threads reach a common synchronization point</p> Signup and view all the answers

    What does 'Mutual exclusion' aim to achieve in parallel computing?

    <p>Preventing multiple threads from accessing the same critical region simultaneously</p> Signup and view all the answers

    What role does 'omp_get_thread_num()' play in achieving synchronization in parallel computing?

    <p>Assigning unique identifiers to each thread for proper ordering</p> Signup and view all the answers

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