18 Questions
What is the computational intensity in the context of matrix multiplication?
O((M_{fast})^{1/2})
Which data layout works well for any cache size but incurs expensive index calculations to find A[i,j]?
Z-Morton order
According to Hong & Kung's theorem, what is the relationship between the number of words moved between fast and slow memory and the computational intensity?
#words moved = O( (n^3) / (M_{fast})^{1/2} )
In recursive matrix multiplication, at what point should recursion be cut off?
1x1
Which matrix order works well for any cache size but incurs expensive index calculations?
Hilbert curve order
What is the key focus of optimizing latency and bandwidth in parallel matrix multiplication according to the lecture?
Reducing communication overhead
What is the key factor in determining the minimum possible time for a computation in a machine with fast and slow memory levels?
Number of memory elements moved between fast and slow memory
In the context of matrix multiplication, what does 'CI' stand for?
Computational Intensity
How many arithmetic operations are involved in the recursive matrix multiplication function RMM when n = 1?
$1$
What is the primary purpose of defining the function C = RMM(A, B, n) recursively in matrix multiplication?
To break down large matrix multiplications into smaller, more manageable sub-multiplications
In the context of matrix multiplication, what does 'tm' represent in the machine balance equation?
Time per slow memory operation
Which factor directly influences the balance of a computation in terms of memory movement between fast and slow memory levels?
memory elements moved between fast and slow memory
What is the significance of the 'Newer Record' of 2.3729269?
It represents a reduction in the number of arithmetic operations needed for matrix multiplication.
Why is it mentioned that fast methods, besides Strassen's algorithm, may require unrealistically large n?
To suggest the need for further research in reducing data movement in matrix operations.
What does the term 'Computational Intensity' refer to in the context of matrix operations?
The ratio of computational work to data movement in matrix calculations.
Why is it important to extend the lower bound on the number of words moved in certain algorithms?
To improve the stability and efficiency of numerical calculations.
In matrix multiplication, what does 'BLAS1' refer to?
Matrix-vector operations involving dot product, saxpy, etc.
What role do vendors and others play in optimizing Basic Linear Algebra Subroutines (BLAS)?
Supplying optimized implementations of industry standard interfaces for matrix calculations.
Test your understanding of Applications of Parallel Computers, particularly on Matrix Multiplication and the Roofline Model as discussed in Lecture 4 of the course DS 642. This quiz covers concepts like memory hierarchy, balancing memory elements between fast and slow memory, and time optimization strategies.
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