Removing the continuum components and adding in the wavelength dependence produces a matrix equation with which to do the inversion:
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As detailed in inverted " ( a mathematical formula to solve a matrix equation ) to help estimate historic surface temperatures.
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Solution of the matrix equation " Ra " = " r " is computationally a relatively expensive process.
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In this case, the solution can be found by applying two successive rotations to the matrix equation above, of the form
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In fact what has been done here is multiply the matrix equation "'b "'} } on the left by.
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This matrix equation is very simple to implement and requires only that the 2D FT of the basis functions be computed, preferably in closed form.
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There are several different methods available for evaluating a matrix equation including but not limited to Cholesky decomposition and the brute force evaluation of systems of equations.
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For all ports the reflected power waves may be defined in terms of the S-parameter matrix and the incident power waves by the following matrix equation:
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Using a dual wavelength system, measurements for oxy-Hb ( HbO 2 ) and Deoxy-Hb ( Hb ) can be solved from the matrix equation:
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Next, by applying adiabatic boundary conditions at the lateral walls and fix temperature at the bottom ( heat sink temperature ), thermal impedance matrix equation is derived:
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