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Th3HoopMan
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Could anybody link me to some good examples on how to go about doing them? I honestly have no idea how to go about doing these two types of problems.
It's not clear what you are looking for here.Th3HoopMan said:Could anybody link me to some good examples on how to go about doing them? I honestly have no idea how to go about doing these two types of problems.
Examples of problems which can be solving using QRSteamKing said:It's not clear what you are looking for here.
Do you want to know how to develop QR decomposition using HH & Givens Transforms?
Or
Are you looking for examples of problems which can be solved using QR decomposition?
Just about any regression problem where the number of data points exceeds the degree of the curve being fitted.Th3HoopMan said:Examples of problems which can be solving using QR
Thank you!SteamKing said:Just about any regression problem where the number of data points exceeds the degree of the curve being fitted.
You use QR to find the minimum of the residuals in place of forming the normal equations.
Here is an example using linear least squares:
http://www.uta.edu/faculty/rcli/Teaching/math5392/NotesByHyvonen/lecture3.pdf
Note: actual problem starts on p. 11, but there is a good intro. in pp. 1-10.![]()
QR Decomposition is a mathematical technique used to decompose a matrix into an orthogonal matrix (Q) and an upper triangular matrix (R). It is commonly used in linear algebra and is particularly useful for solving systems of linear equations and finding eigenvalues and eigenvectors.
Householder Transformations are a type of matrix transformation used in the QR Decomposition process. They involve reflecting a vector or matrix across a hyperplane, resulting in a new vector or matrix that is orthogonal to the original one.
Givens Transformations are another type of matrix transformation used in QR Decomposition. They involve rotating a matrix or vector in a plane to eliminate certain elements, resulting in a new matrix or vector that is orthogonal to the original one.
Householder and Givens Transformations are used in QR Decomposition because they are efficient and stable methods for decomposing a matrix into orthogonal and upper triangular matrices. These transformations also preserve the original matrix's structure, making it easier to solve linear equations and perform other operations.
QR Decomposition w/ Householder and Givens Transformations has many practical applications in fields such as engineering, physics, and finance. It is commonly used for data analysis, signal processing, image recognition, and optimization problems. It is also used in computer graphics and simulations to solve systems of linear equations efficiently.