mf_hilbert.hlp

是一个经济学管理应用软件 很难找的 但是经济学学生又必须用到

{smcl}
{* 28mar2005}{...}
{bf:help mata Hilbert()}
{hline}
{* index Hilbert()}{...}

{title:Title}

{p 4 4 2}
{bf:[M-5] Hilbert() -- Hilbert matrices}


{title:Syntax}

{p 8 12 2}
{it:real matrix} 
{cmd:Hilbert(}{it:real scalar n}{cmd:)}

{p 8 12 2}
{it:real matrix} 
{cmd:invHilbert(}{it:real scalar n}{cmd:)}


{title:Description}

{p 4 4 2}
{cmd:Hilbert(}{it:n}{cmd:)}
returns the {it:n x n} Hilbert matrix, defined as 
matrix {it:H} with elements {it:H}[{it:i},{it:j}]=1/({it:i}+{it:j}-1).

{p 4 4 2}
{cmd:invHilbert(}{it:n}{cmd:)}
returns the inverse of the {it:n x N} Hilbert matrix, defined as 
the matrix with elements
(-1)^({it:i}+{it:j})*({it:i}+{it:j}-1)*comb({it:n}+{it:i}-1,
{it:n}-{it:j})*comb({it:n}+{it:j}-1,
{it:n}-{it:i})*comb({it:i}+{it:j}-2, {it:i}-1)^2. 


{title:Remarks}

{p 4 4 2}
{cmd:Hilbert(}{it:n}{cmd:)} and 
{cmd:invHilbert(}{it:n}{cmd:)}
are used in testing Mata.  
Hilbert matrices are notoriously ill conditioned.  
The determinants of the first five Hilbert matrices are
1, 1/12, 1/2,160, 1/6,048,000, and 1/266,716,800,000.


{title:Conformability}

    {cmd:Hilbert(}{it:n}{cmd:)}, {cmd:invHilbert(}{it:n}{cmd:)}:
		{it:n}:  1 {it:x} 1
	   {it:result}:  trunc({it:n}) {it:x} trunc({it:n})


{title:Diagnostics}

{p 4 4 2}
None.


{title:Source code}

{p 4 4 2}
{view hilbert.mata, adopath asis:hilbert.mata},
{view invhilbert.mata, adopath asis:invhilbert.mata}
    

{title:Also see}

{p 4 13 2}
Manual:  {hi:[M-5] Hilbert()}

{p 4 13 2}
Online:  help for 
{bf:{help m4_matrix:[M-4] matrix}}
{p_end}