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Functions
static void	givens (double x, double y, double c, double s)

void	solve_hessenberg (double H[nl *nl], double x[nl])

Function Documentation

◆ givens()

static void givens	(	double	x,
		double	y,
		double *	c,
		double *	s
	)

inlinestatic

A solver for Hessenberg systems

An Hessenberg matrix is an "almost triangular" matrix i.e. the sum of a triangular matrix and a tridiagonal matrix.

The function below solves \(Hx=b\) where \(H\) is an upper Hessenberg matrix of rank \(n\). The right-hand side \(b\) is given as vector \(x\) and is replaced by the solution. \(H\) is given as a one dimensional array where each matrix element is indexed as \(H_{ij} = H[in+j]\).

References

@book{henry1994,
  title={The shifted Hessenberg system solve computation},
  author={Henry, Greg},
  year={1994},
  publisher={Cornell Theory Center, Cornell University},
  url={https://pdfs.semanticscholar.org/df75/8d16317f246ac4049a1569b6f56510a4add7.pdf}
}

Definition at line 29 of file hessenberg.h.

References c, s, sign2(), sq(), t, x, and y.

Referenced by solve_hessenberg().

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◆ solve_hessenberg()

void solve_hessenberg	(	double	H[nl *nl],
		double	x[nl]
	)

Definition at line 54 of file hessenberg.h.

References a, c, givens(), i, k, l, nl, s, v, and x.

Referenced by relax_nh().