Over the course of the last three months we have added many important improvements and bug fixes into toolbox. We decided to produce the new official release as it contains critical updates for all platforms (even though eigensolver for large sparse matrices is not included yet).

Here is the main changes:

1. The Core: Multithreading manager has been updated with better load-balancing and non-blocking synchronization. This results in 15-20% performance boost in all operations with dense matrices, even including the matrix multiplication.
2. Eigenvalues.
   • Speed of unsymmetric generalized eigen-decomposition has been improved. Now toolbox uses blocked version of Hessenberg tridiagonal reduction^[1] which gives us timings lower by 20%.
   • Speed of symmetric eigen-decomposition has been boosted up as well. All cases are covered, including the standard and generalized problems in quadruple and arbitrary precision modes and both complexities.

     Actual speed-up factor depends on number of cores and matrix size. In our environment Core i7/R2015a/Win7 x64 we see x3 times ratio for 1Kx1K matrix:

     mp.Digits(34)
     A = mp(rand(1000)-0.5);
     A = A+A';
      
     % Previous versions
     tic; eig(A); toc;
     Elapsed time is 48.154 seconds.
      
     % 3.9.0.9919
     tic; eig(A); toc;      % x3.4 times faster
     Elapsed time is 14.212 seconds.

     Speed-up is even higher for other precision levels:

     mp.Digits(50)
     A = mp(rand(1000)-0.5);
     A = A+A';
      
     % Previous versions
     tic; eig(A); toc;
     Elapsed time is 204.431 seconds.
      
     % 3.9.0.9919
     tic; eig(A); toc;      % x5.3 times faster
     Elapsed time is 38.534 seconds.

     In fact, all operations with dense symmetric/Hermitian and SPD/HPD matrices have became faster: chol, inv, det, solvers, etc. For example, speed-up ratio for inv is up to x10 times depending on matrix structure and number of cores.

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