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A method for computing the partial singular value decomposition.

¹Department of Communications, Communications Research Center, Box 11490, Station H, Ottawa, Ont., Canada K2H 8S2.

IEEE Transactions on Pattern Analysis and Machine Intelligence

|April 14, 2012

Summary

This study introduces a novel method for partial singular value decomposition, ideal for low-rank matrices. The technique is computationally efficient, simple to implement, and requires minimal memory.

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Area of Science:

Numerical Analysis
Linear Algebra
Matrix Computations

Background:

Singular Value Decomposition (SVD) is a fundamental matrix factorization technique.
Computing the full SVD can be computationally expensive for large matrices.
Partial SVD is often sufficient when only the dominant singular values/vectors are needed.

Purpose of the Study:

To present a new method for computing the partial singular value decomposition (SVD) of a matrix.
To address scenarios where matrices are known to be of low rank.
To focus on extracting only the principal singular vectors.

Main Methods:

A novel algorithm for partial singular value decomposition.
Implementation in integer arithmetic.
Analytical and simulation-based investigation of convergence properties.

Main Results:

The described method is suitable for low-rank matrix problems.
It efficiently computes principal singular vectors.
The technique demonstrates simplicity and modest memory requirements.

Conclusions:

The proposed partial SVD method offers an efficient and practical solution for specific matrix problems.
Its ease of implementation and low memory footprint make it valuable.
Further analysis confirms its convergence properties.