DeepAI AI Chat
Log In Sign Up

Solving The Ordinary Least Squares in Closed Form, Without Inversion or Normalization

01/04/2023
by   Vered Senderovich Madar, et al.
Cedars-Sinai
0

By connecting the LU factorization and the Gram-Schmidt orthogonalization without any normalization, closed-forms for the coefficients of the ordinary least squares estimates are presented. Instead of using matrix inversion explicitly, each of the coefficients is expressed and computed directly as a linear combination of non-normalized Gram-Schmidt vectors and the original data matrix and also in terms of the upper triangular factor from LU factorization. The coefficients may computed iteratively using backward or forward algorithms given.

READ FULL TEXT

page 1

page 2

page 3

page 4

11/25/2022

Secure Distributed Gram Matrix Multiplication

The Gram matrix of a matrix A is defined as AA^T (or A^TA). Computing th...
08/25/2017

Inverse of a Special Matrix and Application

The matrix inversion is an interesting topic in algebra mathematics. How...
01/20/2021

Factorization in Call-by-Name and Call-by-Value Calculi via Linear Logic (long version)

In each variant of the lambda-calculus, factorization and normalization ...
05/16/2022

Post-Modern GMRES

The GMRES algorithm of Saad and Schultz (1986) for nonsymmetric linear s...
10/09/2017

Network Embedding as Matrix Factorization: Unifying DeepWalk, LINE, PTE, and node2vec

Since the invention of word2vec, the skip-gram model has significantly a...
11/30/2018

On least squares problems with certain Vandermonde--Khatri--Rao structure with applications to DMD

This paper proposes a new computational method for solving structured le...
12/10/2021

Inversion of band-limited discrete Fourier transforms of binary images: Uniqueness and algorithms

Inversion of the two-dimensional discrete Fourier transform (DFT) typica...