Hilbert matrix
In linear algebra, a Hilbert matrix, introduced by Hilbert (), is a square matrix with entries being the unit fractions For example, this is the 5 × 5 Hilbert matrix: The Hilbert matrix can be regarded as derived from the integral that is, as a Gramian matrix for powers of x. It arises in the least squares approximation of arbitrary functions by polynomials. The Hilbert matrices are canonical examples of ill-conditioned matrices, making them notoriously difficult to use in numerical computation. For example, the 2-norm condition number of the matrix above is about 4.8 · 105.
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Hilbert matrix
In linear algebra, a Hilbert matrix, introduced by Hilbert (), is a square matrix with entries being the unit fractions For example, this is the 5 × 5 Hilbert matrix: The Hilbert matrix can be regarded as derived from the integral that is, as a Gramian matrix for powers of x. It arises in the least squares approximation of arbitrary functions by polynomials. The Hilbert matrices are canonical examples of ill-conditioned matrices, making them notoriously difficult to use in numerical computation. For example, the 2-norm condition number of the matrix above is about 4.8 · 105.
has abstract
25بك المحتوى هنا ينقصه الاستشه ...... عد 5 × 5 :
* 32xبوابة رياضيات
@ar
De Hilbert-matrix van de orde ...... ordt, hoe scherper de test is.
@nl
Die Hilbert-Matrix der Ordnung ...... gt ist, beurteilt werden soll.
@de
En algèbre linéaire, une matri ...... sont donc définies positives.
@fr
En álgebra lineal, una Matriz ...... es aproximadamente 4.8 · 105.
@es
In linear algebra, a Hilbert m ...... trix above is about 4.8 · 105.
@en
In matematica, una matrice di ...... lla matrice H o del vettore v.
@it
Macierz Hilberta - macierz kwa ...... zatem praktycznie niemożliwe.
@pl
В линейной алгебре, матрицей Г ...... ённой матрицы равно 4.8 · 105.
@ru
在线性代数中，希尔伯特矩阵是一种系数都是單位分數的方块矩阵。 ...... 当范数为 矩阵范数时希尔伯特矩阵的条件数大约是 ，远大于1。
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Wikipage revision ID
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comment
25بك المحتوى هنا ينقصه الاستشه ...... عد 5 × 5 :
* 32xبوابة رياضيات
@ar
De Hilbert-matrix van de orde ...... het berekenen van de inverse
@nl
Die Hilbert-Matrix der Ordnung ...... t werden: , . Im Spezialfall .
@de
En algèbre linéaire, une matri ...... er d'un déterminant de Cauchy.
@fr
En álgebra lineal, una Matriz ...... es arbitrarias por polinomios.
@es
In linear algebra, a Hilbert m ...... trix above is about 4.8 · 105.
@en
In matematica, una matrice di ...... lla matrice H o del vettore v.
@it
Macierz Hilberta - macierz kwa ...... zatem praktycznie niemożliwe.
@pl
В линейной алгебре, матрицей Г ...... о обусловленности относительно
@ru
在线性代数中，希尔伯特矩阵是一种系数都是單位分數的方块矩阵。 ...... 当范数为 矩阵范数时希尔伯特矩阵的条件数大约是 ，远大于1。
@zh
label
Hilbert matrix
@en
Hilbert-Matrix
@de
Hilbert-matrix
@nl
Macierz Hilberta
@pl
Matrice de Hilbert
@fr
Matrice di Hilbert
@it
Matriz de Hilbert
@es
Матрица Гильберта
@ru
مصفوفة هيلبرت
@ar
ヒルベルト行列
@ja