Description Usage Arguments Details Methods Author(s) See Also

solve-methods using generalized inverses for various types of matrices

1 2 3 4 5 6 7 8 9 | ```
solve(a,b, ...)
## S4 method for signature 'ANY,ANY'
solve(a, b, generalized =
getdistrOption("use.generalized.inverse.by.default"), tol = 1e-10)
## S4 method for signature 'PosSemDefSymmMatrix,ANY'
solve(a, b, generalized =
getdistrOption("use.generalized.inverse.by.default"), tol = 1e-10)
## S4 method for signature 'PosDefSymmMatrix,ANY'
solve(a, b, tol = 1e-10)
``` |

`a` |
matrix to be inverted / to be solved for RHS. |

`b` |
a numeric or complex vector or matrix giving the right-hand
side(s) of the linear system. If missing, |

`...` |
further arguments to be passed to specific methods (see |

`generalized` |
logical: should generalized / Moore-Penrose inverses be used? By default uses
the corresponding global option to be set by |

`tol` |
the tolerance for detecting linear dependencies in the
columns of |

The method for the Moore-Penrose inverse for
`signature(a = "PosSemDefSymmMatrix", b = "ANY")`

uses `eigen`

to find the eigenvalue
decomposition of `a`

and then simply "pseudo-inverts" the corresponding diagonal matrix built from
`eigen(a)$values`

, while for `signature(a = "ANY", b = "ANY")`

it uses the svd
decomposition of `a`

and then simply "pseudo-inverts" the corresponding diagonal matrix built from
`svd(a)$d`

.

- solve
`signature(a = "ANY", b = "ANY")`

: tries to evaluate`solve.default`

method from base in classical way; if this gives an error, this one is returned if`generalized`

is`TRUE`

, else it will then return*a^-b*where*a^-*is the pseudo or Moore-Penrose inverse of*a*.- solve
`signature(a = "PosSemDefSymmMatrix", b = "ANY")`

: evaluates*a^-b*where*a^-*is the pseudo or Moore-Penrose inverse of*a*.- solve
`signature(a = "PosDefSymmMatrix", b = "ANY")`

: evaluates solve method from base in classical way.

Peter Ruckdeschel peter.ruckdeschel@uni-oldenburg.de

`solve`

for the default method, `eigen`

and `svd`

for the pseudo inversion

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