Parallel Computing: Matrix-Matrix Multiplication

Which of the following is correct about linear equations?

A system of linear equations of the form Ax = b can be solved by using a factorization algorithm. An alternate form of Gaussian elimination is the column-oriented form.

Which of the following is correct about dense matrix algorithms?

Algorithms that involve matrices and vectors are applied in several numerical and non-numerical contexts. Dense matrix algorithms can be easily adapted to rectangular matrices.

Which of the following is an accurate statement about Cannon's algorithm? Which of the following is correct about Cannon's algorithm?

Blocks can be systematically rotated among the processes after every submatrix multiplication. Cannon's algorithm is a memory-efficient version of the simple algorithm. The first communication step of the algorithm aligns the blocks of the matrices. The initial alignment of the two matrices involves a row-wise and a column-wise circular shift.

Which of the following is correct about a column-oriented Gaussian elimination algorithm?

Column-wise 1-D partitioning is more suitable than row-wise 1-D partitioning. It is more useful than the row-oriented algorithm. A system of linear equations that result from the subtraction of a multiple of an equation from other equations is equivalent to the original system.

In the row-wise 1-D partitioning, the initial distribution consists of which of the following?

Each process having a row of n * n matrix

Which of the following is correct about simple parallel algorithms?

In a simple parallel algorithm, blocks are mapped into a logical mesh of processes. An all-to-all broadcast of matrix Y's blocks is performed in each column.

Which of the following is correct about all-to-one reduction?

In an all-to-one reduction operation, the participating processes start with a buffer.

Which of the following is correct about a DNS algorithm? Which of the following is an accurate statement about the DNS algorithm?

It has a variant that uses fewer than n3 processes. It has three main communication steps. It is a cube with faces that correspond to A, B, and C. It is named after its creators: Dekel, Nassimi, and Sahni. All-to-one reduction along the k axis It is a parallel algorithm that performs matrix multiplication. It uses 3-D partitioning.

Which of the following is a step in a simple parallel algorithm?

Local multiplications

Which of the following is correct about 1-D partitioning?

Partial pivoting has no significant effect on the performance of 1-D partitioning. Performing partial pivoting is straightforward with row-wise partitioning.

Which of the following is correct about 2-D partitioning?

Partial pivoting may lead to considerable performance degradation in parallel Gaussian elimination with 2-D partitioning. In a pipelined version of Gaussian elimination with 2-D partitioning, fronts that correspond to various iterations move from the top-left to the bottom-right. In the case of 2-D partitioning of the coefficient matrix, partial pivoting seriously restricts pipelining.

Which of the following is correct about the scalability of an all-to-all broadcast?

Scalability measures the ability to increase the speedup in the function of p.