Search Results

I have a $N \times N$ matrix $A$ where $U$ is stored in the upper triangle (plus diagonal), and $L$ is stored in the lower triangle. … I want to store the product $U L^T$ in-place in the upper triangle of the matrix $A$. …

Now multiplying a diagonal matrix by a trapezoidal gives a trapezoidal matrix, so the problem becomes solving the trapezoidal least squares problem $$ (D_i L) z = y $$ My question is how can this trapezoidal …

I need to compute a matrix-matrix product, $A^T B$, where $A$ is $n \times r$ sparse, and $B$ is $n \times q$ dense. The number of rows $n$ is far larger than both $r$ and $q$. … In fact $n$ is so large I cannot store the entire matrix $B$ in memory, so I build it one row at a time and update the matrix product $A^T B$ accordingly. …

The bottleneck of the code is when I need to update the matrix $A$. I give each thread its own matrix A to update and then sum them all together at the end for the final A. … I added a #if flag to enable/disable the matrix copy operation which is the slow part. …

In brief, recursive LU on a $M \times N$ matrix $A$ proceeds by partitioning the matrix into 4 blocks: \begin{align} \pmatrix{A_{11} & A_{12} \\ A_{21} & A_{22}} &= \pmatrix{L_{11} & 0 \\ L_{21} & L_{22 … However, for your specialized matrix, you should pick $A_{11}$ to be a square upper triangular matrix. …

I want to compute the matrix $$ A = \sum_{i=1}^N v_i v_i^T $$ where each $v_i$ is a given vector of length $2500$, so that $A$ is $2500 \times 2500$, and my $N$ is about 2 million. … Currently, I am choosing $\textrm{block_size} = 50000$, which I only chose so that the total size of the $W_k$ storage matrix is 1GB ($50000 \times 2500 \times 8 = 1 GB$). …

I have a set of measurements $y_i$, $1 \leq i \leq N$, and I want to model these measurements with a linear model. I have two possible models I can use, $$ y \approx A c $$ and $$ y \approx B d $$ whe …