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numeric::spectralRadius

Spectral radius of a matrix

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Syntax

numeric::spectralRadius(A, <x0>, <n>, <mode>, <ReturnType = t>, <NoWarning>)

Description

numeric::spectralRadius and numeric::spectralradius are equivalent. For details and examples, see numeric::spectralradius.

Environment Interactions

The function is sensitive to the environment variable DIGITS, which determines the numerical working precision.

Parameters

A

An m×m array of domain type DOM_ARRAY or DOM_HFARRAY or a matrix of category Cat::Matrix

x0

A starting vector: a one-dimensional array, or an hfarray, or a list of length m. Also two-dimensional arrays (array(1..m, 1..1, ...), hfarray(1..m, 1..1, ...)) and matrices representing vectors are accepted.

n

The maximal number of iterations: a positive integer. The default value is 1000.

mode

One of the flags Hard, HardwareFloats, Soft, or SoftwareFloats

Return Values

A list [lambda, x, residue] is returned. The floating-point number lambda is an approximation of the eigenvalue of largest absolute value. The vector x is a numerical eigenvector corresponding to lambda. residue is a floating-point number indicating the numerical quality of lambda and x.

If no return type is requested via the ReturnType option, the type of the returned vector x coincides with the type of the input vector x0 (i.e., it is a one-dimensional array of type DOM_ARRAY or DOM_HFARRAY, respectively, or a list, or a column vector of type matrix or densematrix. If no starting vector is specified, the type of x is determined by the type of A.

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