com.numericalmethod.suanshu.matrix.doubles.matrixtype
Class HilbertMatrix

java.lang.Object
  com.numericalmethod.suanshu.matrix.doubles.matrixtype.MatrixMathImpl<T>
      com.numericalmethod.suanshu.matrix.doubles.matrixtype.MatrixStorageImpl<SymmetricMatrix>
          com.numericalmethod.suanshu.matrix.doubles.matrixtype.dense.triangle.SymmetricMatrix
              com.numericalmethod.suanshu.matrix.doubles.matrixtype.HilbertMatrix

All Implemented Interfaces:

DeepCopyable, AbelianGroup<Matrix>, Monoid<Matrix>, Ring<Matrix>, Matrix, MatrixAccessor, MatrixRing, Densifiable, MatrixDimension

public class HilbertMatrix
extends SymmetricMatrix

A Hilbert matrix, H, is a symmetric matrix with entries being the unit fractions

H[i][j] = 1 / (i + j -1)

See Also:

Wikipedia: Hilbert matrix

Field Summary

Fields inherited from class com.numericalmethod.suanshu.matrix.doubles.matrixtype.dense.triangle.SymmetricMatrix

dim

Constructor Summary

HilbertMatrix(int dim)
Construct a Hilbert matrix of dimension dim * dim.

Method Summary

double	det() The determinant of a Hilbert matrix is the reciprocal of an integer.
java.math.BigInteger	invdet() One over the determinant of H.

Methods inherited from class com.numericalmethod.suanshu.matrix.doubles.matrixtype.dense.triangle.SymmetricMatrix

add, deepCopy, equals, get, getColumn, getRow, hashCode, minus, ONE, scaled, set, t, toDense, toString, ZERO

Methods inherited from class com.numericalmethod.suanshu.matrix.doubles.matrixtype.MatrixStorageImpl

getMatrixData, setMatrixData

Methods inherited from class com.numericalmethod.suanshu.matrix.doubles.matrixtype.MatrixMathImpl

add, call, getSample, minus, multiply, multiply, nCols, nRows, opposite, setColumn, setColumn, setRow, setRow

Methods inherited from class java.lang.Object

clone, finalize, getClass, notify, notifyAll, wait, wait, wait

Constructor Detail

HilbertMatrix

public HilbertMatrix(int dim)

Construct a Hilbert matrix of dimension dim * dim.

Parameters:

dim - Hilbert matrix dimension, i.e., the number of rows or number of columns

Method Detail

invdet

public java.math.BigInteger invdet()

One over the determinant of H.

   1
 -----
  |H|
 

Returns:

one over the determinant of H

det

public double det()

The determinant of a Hilbert matrix is the reciprocal of an integer.

Returns:

the determinant

See Also:

OEIS: sequence A005249