num::hessenberg_resolvent

Defined in header <linear/solvers/hessenberg_resolvent.hpp>

class hessenberg_resolvent;

\(A\) reduced once to \(A = QHQ^T\), ready to factor \(sI - A\) for any shift.

The reduction costs \(O(n^3)\) once; shift(R, s) then costs \(O(n^2)\) per shift:

hessenberg_resolvent R(A);     auto F = shift(R, s);     // sI - A, factored     solve(F, b, x);           // x = (sI - A)^{-1} b, as many times as needed

Copies share the reduction, and each shifted factor keeps it alive.

Members

member	description
explicit hessenberg_resolvent(const mat<real> &A)
explicit hessenberg_resolvent(const spmat &A)
explicit hessenberg_resolvent(hessenberg_decomposition decomp)
idx size() const noexcept
const hessenberg_decomposition &decomposition() const noexcept