This directory collects Matlab functions, scripts and
benchmark test examples for performing reduced-order modeling 
of dynamical systems, reported in the following following 
tutorial and survey paper: 

  Z. Bai, Krylov Subspace Techniques for Reduced-Order Modeling
  of Large-Scale Dynamical Systems, Applied Numerical Mathematics,
  Volume 43, Issues 1-2, October 2002, Pages 9-44.

Try! Have Fun! Your comments (good or bad) are welcome!

Zhaojun Bai   bai@cs.ucdavis.edu

================================================================

Drivers/Demos
---------------------
   driver_awebook.m   
   driver_peec.m  
   driver_brake834.m  
 
Main Routine for reduced-order modeling by PVL 
----------------------------------------------
   romlin.m    linear system


Subroutines 
-----------
   lanczos.m   basic Lanczos process
   lanczos2.m  basic Lanczos process, but the matrix A is accessed 
               in factor forms via calling matvec.m, matvect.m
   tridiag.m   form the tridiagonal matrix T in Lanczos process
   matvec.m    matrix-vector multiplications, called by lanczos2.
   matvect.m 

Test data 
---------

   awebookeg.m (linear system) 
      A small RLC network described in the book ``Asymptotic
      Waveform Evaluation'' by E. Chiprout and M. S. Nakhla, 
      Kluwer Academic Publishers, 1994. 
      [Shown in section 2.7] 

   ex306v4.mat (linear system) 
      the famous PEEC circuit, a benchmark example. 
      [Shown in section 2.5]  

   brake834M.mat, brake834K.mat (linear system), 
      the brake example as show in Bai's paper. 
      [Shown in section 2.5] 
      Note: Both K and M are spd, in fact, M is diagonal,
            condest(M) = 17, condest(K) = 1.5e+5;  
            R = chol(M); A = (R'\K)/R; condest(A) = 4.9638e+05
            d = eigs(A,5,'SM') fails convergence after 300 iterations. 
            by full eigensolver, eig(full(A)), 10 smallest eigenvalues: 
               9.4981e+07
   	       1.0540e+08
   	       1.2875e+08
   	       1.5001e+08
               1.6093e+08
               2.1635e+08
               2.8378e+08
               4.1205e+08
               5.4246e+08
               5.4257e+08 

   ex1346.mat (linear system) 
      the extracted RC circuit example.
      [Shown in section 2.10] 

   resonator.mat  (second-order system) 
      Linear-drive multi-mode resonator 
      [Shown in section 3.2] 

   y6103f.mat   (second-order system) 
      Finite element model of a shaft on bearing supports with a damper 
      [Shown in section 3.3]