Java Multithreading and Parallel Programming Masterclass - Parallel Matrix Multiplication - The Optimal Way

The lecture introduces block matrix multiplication, a parallelization approach for matrix multiplication. It explains the concept, benefits, and implementation details, focusing on using tasks and semaphores for synchronization. The lecture also compares the performance of this approach with a serial version, highlighting its efficiency and memory trade-offs.

What is the key mathematical observation that block matrix multiplication is based on?

• Gaussian elimination

• Block matrix multiplication

• Eigenvalue decomposition

• Matrix inversion

Under what condition can block matrix multiplication be applied?

• Matrices must be splittable into four blocks

• Matrices must be invertible

• Matrices must be square

• Matrices must have equal dimensions

How many multiplication tasks are used in the parallelization strategy for block matrix multiplication?

• Four

• Six

• Eight

• Ten

What is the role of the addition tasks in the parallelization strategy?

• To subtract the blocks

• To multiply blocks

• To add the results of multiplication tasks

• To divide the blocks

What is the purpose of using semaphores in the implementation of block matrix multiplication?

• To simplify code

• To decrease execution time

• To synchronize tasks

• To increase memory usage

What is the trade-off made in the implementation of block matrix multiplication?

• Complexity for simplicity

• Memory for execution time

• Precision for speed

• Speed for accuracy

How is the result of a multiplication task stored in the implementation?

• In a temporary file

• Directly in the output array

• In intermediate arrays

• In a database

What is the main drawback of the block parallel matrix multiplication approach?

• It requires more memory

• It is more complex to implement

• It is slower than the serial version

• It is less accurate

How does the block parallel matrix multiplication compare to the serial version in terms of speed?

• It is slightly faster

• It is about the same

• It is slower

• It is more than twice as fast

What can be adjusted to potentially improve the performance of the block matrix multiplication?

• The type of semaphores

• The number of addition tasks

• The number of threads

• The size of the matrices