LSQR Meaning and
Definition
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LSQR stands for "Least Squares QR" and it refers to a numerical computation algorithm used in the field of linear algebra and numerical analysis. LSQR is primarily employed to solve systems of linear equations in an efficient manner.
The LSQR method is specifically designed to tackle overdetermined or underdetermined systems of linear equations for large and sparse matrices. It combines the use of QR factorization, which decomposes a matrix into its orthogonal and upper triangular components, with the least squares technique. The goal is to minimize the sum of the squares of the differences between the left-hand side and right-hand side of the equations.
In LSQR, the algorithm iteratively constructs approximations to the solution vector by solving a sequence of least squares subproblems. At each iteration, LSQR computes matrix-vector products using the given matrix and its transpose, thereby eliminating the explicit calculation of the matrix itself. This makes LSQR particularly useful for large-scale problems where the matrix storage is not feasible.
The key advantage of LSQR is its ability to solve linear systems in a stable and efficient manner, even when the matrices involved are ill-conditioned or singular. It is known for its numerical robustness and scalability, making it popular in various applications such as image reconstruction, signal processing, and data analysis. LSQR has found significant application in the fields of computational science and engineering due to its accuracy and computational efficiency.
Common Misspellings for LSQR
- psqr
- osqr
- lzqr
- lwqr
- ls1r
- ls2r
- lsq5
- lsq4
- klsqr
- lksqr
- plsqr
- lpsqr
- olsqr
- losqr
- lasqr
- lsaqr
- lzsqr
- lszqr
- lxsqr
- lsxqr
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