update paper.md

paper.md

@@ -90,9 +90,8 @@ Libcientific tests range from simple matrix-vector multiplication to the correct
 # Speed and Memory Comparison
 
 Several simulations of every algorithm in libscientific with data of different sizes (input size) against CPU speed were performed to address the algorithm's performance.
-Looking at their plots, we observe a linear trend, which indicates that the algorithm's time complexity is linear, denoted as O(n) in computational complexity analysis.
-
-
+Looking at the plots for PCA, CPCA, and PLS, we observe a linear trend, which indicates that the algorithm's time complexity is linear, denoted as O(n).
+Instead, MLR shows an O(n³) behavior as expected from the OLS algorithm, which uses a matrix direct inverse approach.
 
 This means that as the input size (often termed "problem size") increases by a constant factor, the execution time also increases proportionally (linear algorithms). 
 Linear algorithms have notable characteristics:
@@ -101,8 +100,11 @@ Linear algorithms have notable characteristics:
 * Constant Work per Input Element: In linear algorithms, each input element is processed continuously. 
 * Stable Performance Impact: Doubling input size roughly doubles execution time, facilitating performance estimation.
 * Optimal Scaling: Linear-time solutions efficiently handle larger inputs.
-
-Hence we have demonstrated that libscientific scales linearly with the data.
+
+|   |   |
+|---|---|
+| ![PCA](https://github.com/gmrandazzo/libscientific/blob/1bfcf13d0310b3e115abd5b15f9add62c37012f0/performance/pca_input_vs_cputime.png) PCA | ![CPCA](https://github.com/gmrandazzo/libscientific/blob/1bfcf13d0310b3e115abd5b15f9add62c37012f0/performance/cpca_input_vs_cputime.png) CPCA |
+| ![PLS](https://github.com/gmrandazzo/libscientific/blob/1bfcf13d0310b3e115abd5b15f9add62c37012f0/performance/pls_input_vs_cputime.png) PLS | ![MLR](https://github.com/gmrandazzo/libscientific/blob/1bfcf13d0310b3e115abd5b15f9add62c37012f0/performance/mlr_input_vs_cputime.png) MLR    |
 
 # Usage