DS 642: Applications of Parallel Computing Lecture 4 Quiz

Play an AI-generated podcast conversation about this lesson

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]?

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?

#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?

1x1 Signup and view all the answers

Which matrix order works well for any cache size but incurs expensive index calculations?

Hilbert curve order Signup and view all the answers

What is the key focus of optimizing latency and bandwidth in parallel matrix multiplication according to the lecture?

Reducing communication overhead Signup and view all the answers

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 Signup and view all the answers

In the context of matrix multiplication, what does 'CI' stand for?

Computational Intensity Signup and view all the answers

How many arithmetic operations are involved in the recursive matrix multiplication function RMM when n = 1?

$1$ Signup and view all the answers

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 Signup and view all the answers

In the context of matrix multiplication, what does 'tm' represent in the machine balance equation?

Time per slow memory operation Signup and view all the answers

Which factor directly influences the balance of a computation in terms of memory movement between fast and slow memory levels?

<h1>memory elements moved between fast and slow memory</h1> Signup and view all the answers

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. Signup and view all the answers

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. Signup and view all the answers

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. Signup and view all the answers

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. Signup and view all the answers

In matrix multiplication, what does 'BLAS1' refer to?

Matrix-vector operations involving dot product, saxpy, etc. Signup and view all the answers

What role do vendors and others play in optimizing Basic Linear Algebra Subroutines (BLAS)?

Supplying optimized implementations of industry standard interfaces for matrix calculations. Signup and view all the answers

DS 642: Applications of Parallel Computing Lecture 4 Quiz

Choose a study mode

Podcast

Questions and Answers