autocorrelation A to K conversion for LPC speech analysis?
After applying a Hamming window to your data I get very similar autocorrelation values:


R = 
   1.6765e+00
   1.5828e+00
   1.3697e+00
   1.0688e+00
   7.4186e-01
   4.6660e-01
   2.5672e-01
   1.2121e-01
   4.9779e-02
   1.6453e-02
   3.1701e-03



You can check your LPC filter coefficients (not the reflection coefficients) by computing the matrix-vector product $\mathbf{R}\mathbf{a}$ where $\mathbf{a}$ is the vector of LPC coefficients and $\mathbf{R}$ is a Toeplitz matrix with the autocorrelation values:

$$\mathbf{R}=\begin{bmatrix}R(0)&amp;R(1)&amp;\ldots &amp;&amp; R(p)\\
R(1)&amp;R(0)&amp;R(1)&amp;\ldots&amp;R(p-1)\\
\vdots&amp; &amp; \ddots &amp; &amp;\vdots\\
R(p) &amp; R(p-1) &amp; \ldots &amp;&amp; R(0)\end{bmatrix}$$

This product must result in a vector with the first element being non-zero, and all the other elements must be zero (up to numerical accuracy).

Using the Octave function [lpc,v,k]=levinson(R(1:11)); with the autocorrelation function given above, I get the following LPC filter coefficients:


lpc =

   1.000000
  -1.370890
  -0.386146
   0.813691
   0.992372
  -0.949576
  -0.642884
   0.427407
   0.515102
  -0.310107
  -0.039544


And these are the corresponding reflection coefficients:


k =

  -0.9440538
   0.6826730
   0.2730461
  -0.1825513
  -0.4886926
   0.1882461
   0.3690086
  -0.0056205
  -0.3648883
  -0.0395440


So we get very similar values from which you can conclude that your code for computing the reflection coefficients from the autocorrelation function is correct.