Nonsymmetric Eigenvalue Problems

This section describes ScaLAPACK routines for solving nonsymmetric eigenvalue problems, computing the Schur factorization of general matrices, as well as performing a number of related computational tasks.

To solve a nonsymmetric eigenvalue problem with ScaLAPACK, you usually need to reduce the matrix to the upper Hessenberg form and then solve the eigenvalue problem with the Hessenberg matrix obtained.

Table "Computational Routines for Solving Nonsymmetric Eigenproblems" lists ScaLAPACK routines for reducing the matrix to the upper Hessenberg form by an orthogonal (or unitary) similarity transformation A= QHQ H , as well as routines for solving eigenproblems with Hessenberg matrices, and multiplying the matrix after reduction.

Computational Routines for Solving Nonsymmetric Eigenproblems
Operation performed General matrix Orthogonal/Unitary matrix Hessenberg matrix
Reduce to Hessenberg form A= QHQ H p?gehrd    
Multiply the matrix after reduction   p?ormhr / p?unmhr  
Find eigenvalues and Schur factorization     p?lahqr , p?hseqr
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