Fast Second-Order Orthogonal Tensor Subspace Analysis for Face Recognition

Algorithm 4

Lanczos procedure.

Input: 𝐴,𝑣 and a dimension 𝑙

Output: Lanczos vectors 𝑣₁,𝑣₂,…,𝑣_𝑙

  (1) Set 𝑣₁=𝑣, 𝛽₁=0 and 𝑣₀=0;

  (2) For 𝑘=1∶𝑙

   (2.1) 𝑤_𝑘=𝐴𝑣_𝑘−𝛽_𝑘𝑣_𝑘−1;

   (2.2) 𝛼_𝑘=𝑤^𝑇_𝑘𝑣_𝑘;

   (2.3) 𝑤_𝑘=𝑤_𝑘−𝛼_𝑘𝑣_𝑘;

   (2.4) 𝛽_𝑘+1=𝑤_𝑘2;

   (2.5) 𝑣_𝑘+1=𝑤_𝑘/𝛽_𝑘+1;

   End For