QR Decomposition without Pivoting¶
Given the matrix \(X\) of size \(n \times p\), the problem is to compute the QR decomposition \(X = QR\), where
\(Q\) is an orthogonal matrix of size \(n \times n\)
\(R\) is a rectangular upper triangular matrix of size \(n \times p\)
The library requires \(n > p\). In this case:
\[\begin{split}X = QR = [Q_1, Q_2] \cdot \begin{bmatrix} R_1 \\ 0 \end{bmatrix} = Q_1 R_1\end{split}\]
where the matrix \(Q_1\) has the size \(n \times p\) and \(R_1\) has the size \(p \times p\).
Computation¶
The following computation modes are available:
Examples¶
Batch Processing:
Online Processing:
Distributed Processing:
Note
There is no support for Java on GPU.
Batch Processing:
Online Processing:
Distributed Processing: