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Efficient Solution of a Toeplitz-Plus-Hankel Coefficient Matrix System of Equations

G.A. Merchant, T.W. Parks

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Abstract

Frequently in signal processing one is faced with situations where a large system of linear equations, with a Toeplitz or a Hankel coefficient matrix, needs to be solved. One efficient way of solving these kinds of equations is by Levinson recursion. The Levinson recursion does not require explicit storage of the Toeplitz (or Hankel) coefficient matrix and the number of multiplies required is proportional to the square of the number of unknowns.

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What this paper is about

Frequently in signal processing one is faced with situations where a large system of linear equations, with a Toeplitz or a Hankel coefficient matrix, needs to be solved. One efficient way of solving these kinds of equations is by Levinson recursion. The Levinson recursion does not require explicit storage of the Toeplitz (or Hankel) coefficient matrix and the number of multiplies required is proportional to the square of the number of unknowns.

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Available abstract

Frequently in signal processing one is faced with situations where a large system of linear equations, with a Toeplitz or a Hankel coefficient matrix, needs to be solved. One efficient way of solving these kinds of equations is by Levinson recursion. The Levinson recursion does not require explicit storage of the Toeplitz (or Hankel) coefficient matrix and the number of multiplies required is proportional to the square of the number of unknowns.

Key concepts: Toeplitz matrix, Levinson recursion, Hankel matrix, Recursion (computer science), Coefficient matrix, Mathematics, Matrix (chemical analysis), Linear system

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