Comparison of approaches to realization of package LAPACK.

Comparison of approaches to realization of package LAPACK.

The new approach which is distinct from Intel MKL, to realization of fast algorithm of diagonalization from package LAPACK is developed. Comparison is of interest for perfection of package Intel MKL.

The following results were attained
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1. A new approach to solution of the algebraic problem of eigenvalues and eigenvectors for a tridiagonal matrix, providing higher speed and considerable RAM saving, was found.
2. A new algorithm of matrix multiplication, ensuring faster transition from the matrix of eigenvectors of a tridiagonal matrix to the matrix of eigenvectors of the initial matrix, was developed.
3. The PalWalkerKahans algorithm was modified, which made the determination of eigenvalues of a tridiagonal matrix several times faster in the case of slow convergence.
4. Block methods were applied to packed matrices, which increased the speed of tridiagonalization of packed matrices by a factor of almost 3 and the speed of transition from the matrix of eigenvectors of a tridiagonal matrix to the matrix of eigenvectors of the initial packed matrix by a factor of 8.
5.The improved implementation of basic algorithms of linear algebra allowed the speed of BLAS Level 2 (IA32 and EM64T) and BLAS Level 3 (IA32) to be increased.

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