Difference between revisions of "Manuals/calci/HILBERT"

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*This function gives matrix of order 3x3 with the property of Hilbert.
 
*This function gives matrix of order 3x3 with the property of Hilbert.
 
*A Hilbert matrix, is a square matrix with entries being the unit fractions.  i.e.,<math>H_{ij}=\frac{1}{i+j-1}.
 
*A Hilbert matrix, is a square matrix with entries being the unit fractions.  i.e.,<math>H_{ij}=\frac{1}{i+j-1}.
*Example for 5x5 Hilbert matrix is: <math><math>\begin{bmatrix}
+
*Example for 5x5 Hilbert matrix is: <math>\begin{bmatrix}
 
1 & \frac{1}{2} & \frac{1}{3} & \frac{1}{4} & \frac{1}{5} \\
 
1 & \frac{1}{2} & \frac{1}{3} & \frac{1}{4} & \frac{1}{5} \\
 
\frac{1}{2} & \frac{1}{3} & \frac{1}{4} & \frac{1}{5} & \frac{1}{6} \\
 
\frac{1}{2} & \frac{1}{3} & \frac{1}{4} & \frac{1}{5} & \frac{1}{6} \\

Revision as of 13:42, 24 April 2015

MATRIX("HILBERT",order)


  • is the order of the Hilbert matrix.

Description

  • This function gives matrix of order 3x3 with the property of Hilbert.
  • A Hilbert matrix, is a square matrix with entries being the unit fractions. i.e.,.
  • The Hilbert matrix is an example of a Hankel matrix.
  • The Hilbert matrix is symmetric and positive definite.
  • Also Hilbert matrices are canonical examples of ill-conditioned matrices, making them notoriously difficult to use in numerical computation.
  • Here MATRIX("hilbert") gives the hilbert matrices with a decimal places .
  • i.e., For 1/2 it will show 0.5, 1/3 will show 0.333 and so on.