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Least Squares with Examples in Signal Processing 1

Ivan Selesnick

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Abstract

Ivan Selesnick March 7, 2013 NYU-Poly These notes address (approximate) solutions to linear equations by least squares. We deal with the ‘easy’ case wherein the system matrix is full rank. If the system matrix is rank deficient, then other methods are needed, e.g., QR decomposition, singular value decomposition, or the pseudo-inverse, [2, 3]. In these notes, least squares is illustrated by applying it to several basic problems in signal processing:

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What this paper is about

Ivan Selesnick March 7, 2013 NYU-Poly These notes address (approximate) solutions to linear equations by least squares. We deal with the ‘easy’ case wherein the system matrix is full rank. If the system matrix is rank deficient, then other methods are needed, e.g., QR decomposition, singular value decomposition, or the pseudo-inverse, [2, 3]. In these notes, least squares is illustrated by applying it to several basic problems in signal processing:

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Available abstract

Ivan Selesnick March 7, 2013 NYU-Poly These notes address (approximate) solutions to linear equations by least squares. We deal with the ‘easy’ case wherein the system matrix is full rank. If the system matrix is rank deficient, then other methods are needed, e.g., QR decomposition, singular value decomposition, or the pseudo-inverse, [2, 3]. In these notes, least squares is illustrated by applying it to several basic problems in signal processing:

Key concepts: Singular value decomposition, Rank (graph theory), Least-squares function approximation, QR decomposition, Linear least squares, Matrix (chemical analysis), Decomposition, Signal processing

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