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Questions and Answers
What is the computational intensity in the context of matrix multiplication?
What is the computational intensity in the context of matrix multiplication?
- O(n^2)
- O(M_{fast})
- O((M_{fast})^{1/2}) (correct)
- O(n^3)
Which data layout works well for any cache size but incurs expensive index calculations to find A[i,j]?
Which data layout works well for any cache size but incurs expensive index calculations to find A[i,j]?
- Recursive layout
- Z-Morton order (correct)
- Col/Row Major
- Blocked-Row Major
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?
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^2)
- #words moved = Ω (n^3)
- #words moved = O(n)
- #words moved = O( (n^3) / (M_{fast})^{1/2} ) (correct)
In recursive matrix multiplication, at what point should recursion be cut off?
In recursive matrix multiplication, at what point should recursion be cut off?
Which matrix order works well for any cache size but incurs expensive index calculations?
Which matrix order works well for any cache size but incurs expensive index calculations?
What is the key focus of optimizing latency and bandwidth in parallel matrix multiplication according to the lecture?
What is the key focus of optimizing latency and bandwidth in parallel matrix multiplication according to the lecture?
What is the key factor in determining the minimum possible time for a computation in a machine with fast and slow memory levels?
What is the key factor in determining the minimum possible time for a computation in a machine with fast and slow memory levels?
In the context of matrix multiplication, what does 'CI' stand for?
In the context of matrix multiplication, what does 'CI' stand for?
How many arithmetic operations are involved in the recursive matrix multiplication function RMM when n = 1?
How many arithmetic operations are involved in the recursive matrix multiplication function RMM when n = 1?
What is the primary purpose of defining the function C = RMM(A, B, n) recursively in matrix multiplication?
What is the primary purpose of defining the function C = RMM(A, B, n) recursively in matrix multiplication?
In the context of matrix multiplication, what does 'tm' represent in the machine balance equation?
In the context of matrix multiplication, what does 'tm' represent in the machine balance equation?
Which factor directly influences the balance of a computation in terms of memory movement between fast and slow memory levels?
Which factor directly influences the balance of a computation in terms of memory movement between fast and slow memory levels?
What is the significance of the 'Newer Record' of 2.3729269?
What is the significance of the 'Newer Record' of 2.3729269?
Why is it mentioned that fast methods, besides Strassen's algorithm, may require unrealistically large n?
Why is it mentioned that fast methods, besides Strassen's algorithm, may require unrealistically large n?
What does the term 'Computational Intensity' refer to in the context of matrix operations?
What does the term 'Computational Intensity' refer to in the context of matrix operations?
Why is it important to extend the lower bound on the number of words moved in certain algorithms?
Why is it important to extend the lower bound on the number of words moved in certain algorithms?
In matrix multiplication, what does 'BLAS1' refer to?
In matrix multiplication, what does 'BLAS1' refer to?
What role do vendors and others play in optimizing Basic Linear Algebra Subroutines (BLAS)?
What role do vendors and others play in optimizing Basic Linear Algebra Subroutines (BLAS)?
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