planBisection.m

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planBisection.m#

If the companion matrix approx fails to find a radius in getRGivenTheta.m, plan B is to use this bisection approach. The initial guesses are the positive real parts from the roots of the companion matrix approach; their imaginary parts were deemed too large in magnitude for them to be trustworthy.

[root, isSuccess] = planBisection(phaseCoeffs, xi, numOscsDivByFreq, theta, guesses)

Inputs#

  • phaseCoeffs : An array of coefficients of the polynomial phase function \(g\).

  • xi : The centre of the non-oscillatory ball.

  • numOscsDivByFreq : This is \(C/\omega\) in getRGivenTheta.m.

  • theta : The angle of the ray.

  • guesses : Initial guesses to consider for multiple bisection approaches.

Outputs#

  • root : The result of the bisection method.

  • isSuccess : Boolean, true if the bisection method found a root.

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