# Is least square fit using Pivoted QR decomposition a single pass or multipass fitting procedure?

2 Ansichten (letzte 30 Tage)
Jay am 21 Okt. 2016
Kommentiert: Jay am 22 Okt. 2016
I was refering, https://www.mathworks.com/help/curvefit/least-squares-fitting.html blog by matlab which tells that "the backslash operator uses QR decomposition with pivoting, which is a very stable algorithm numerically".
My question is, whether surface fitting using Pivoted QR decomposition is a single pass fitting or multipass fitting procedure? If it is trying to minimize the least square then how it is changing the coefficient values for every iteration?
Thanks
##### 0 Kommentare-2 ältere Kommentare anzeigen-2 ältere Kommentare ausblenden

Melden Sie sich an, um zu kommentieren.

### Akzeptierte Antwort

John D'Errico am 21 Okt. 2016
Bearbeitet: John D'Errico am 22 Okt. 2016
Backslash does not use an iterative scheme, if that is what you are asking. As long as your model is linear in the parameters, a linear algebraic solution using pivoted QR is direct. No iterations at all. Some tools like lsqr are iterative. But not backslash.
You are thinking about linear least squares as if it is nonlinear least squares, where an iterative scheme is needed. Again, a model can have higher order terms in it and still be a linear least squares problem, as long as the model is linear in the coefficients.
Are you looking for a proof that it is possible to solve a (linear) least squares estimation using simple linear algebra, i.e., a QR? (Not hard to do, but not on topic for Answers.)
##### 1 Kommentar-1 ältere Kommentare anzeigen-1 ältere Kommentare ausblenden
Jay am 22 Okt. 2016
Thanks. Yes that is what I am looking for. I was wondering how it is getting optimized coefficient values in single pass?

Melden Sie sich an, um zu kommentieren.

### Kategorien

Mehr zu Regression finden Sie in Help Center und File Exchange

### Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by