Difference between revisions of "Manuals/calci/LUDECOMPOSITION"

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*LU Decomposition is the procedure for decomposing any square matrix in to a product of Lower Triangular matrix and Upper Triangular matrix.
 
*LU Decomposition is the procedure for decomposing any square matrix in to a product of Lower Triangular matrix and Upper Triangular matrix.
 
*In LU Decomposition, L stands for Lower Triangular matrix and U stands for Upper Triangular matrix.
 
*In LU Decomposition, L stands for Lower Triangular matrix and U stands for Upper Triangular matrix.
*So A=LU.But sometimes the product includes Permutation Matrix also.
+
*So A=LU.But sometimes the product includes Permutation Matrix also(PA=LU).
 
*LU Decomposition is also called LU Factorization.Here given matrix is split in to lower triangular and Upper triangular matrix.
 
*LU Decomposition is also called LU Factorization.Here given matrix is split in to lower triangular and Upper triangular matrix.
 
**For 2x2 matrix,
 
**For 2x2 matrix,
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=LUDECOMPOSITION(A1:B2)
 
=LUDECOMPOSITION(A1:B2)
{| border="1" cellpadding="2" cellspacing="0"
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{| border="1" cellpadding="5" cellspacing="0"
 
|-
 
|-
 
|
 
|
  1 0
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  1 0
 
||
 
||
  0.6666666666666666 1
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  0.6666666666666666 1
 
|-
 
|-
 
|  
 
|  
  6 3
+
  6 3
 
||  
 
||  
 
  0 1
 
  0 1
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  1 0
 
  1 0
 
|}
 
|}
2. LUDECOMPOSITION([[10,12,16],[-8,-4,15],[20,24,28]])
+
 
 +
{| class="wikitable"
 +
|+Spreadsheet
 +
|-
 +
! !! A !! B !! C   
 +
|-
 +
! 1
 +
| 1 || 2 || 3
 +
|-
 +
! 2
 +
| 4 || 5 || 6
 +
|-
 +
! 3
 +
| 7 || 8 || 9
 +
|}
 +
=LUDECOMPOSITION(A1:C3)
 
{| border="1" cellpadding="5" cellspacing="0"
 
{| border="1" cellpadding="5" cellspacing="0"
 
|-
 
|-
 
|
 
|
1 0 0
+
1 0 0
| -0.4 1 0
+
||
| 0.5 0 1
+
0.5714285714285714 1 0
 +
||
 +
0.14285714285714285 1.999999999999999 1
 
|-
 
|-
 
|  
 
|  
20 24 28
+
7 8 9
|  
+
||  
0 5.600000000000001 26.200000000000003
+
0 0.4285714285714288 0.8571428571428577
|  
+
||  
0 0 2
+
0 0 0
 
|-
 
|-
 
|  
 
|  
0 0 1
+
0 0 1
|  
+
||  
0 1 0
+
0 1 0
|
+
||
1   0 0
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1 0 0
 
|}
 
|}
 +
 +
==Related Videos==
 +
 +
{{#ev:youtube|v=UlWcofkUDDU|280|center|LU Decomposition}}
  
 
==See Also==
 
==See Also==

Latest revision as of 13:30, 29 April 2019

LUDECOMPOSITION (Matrix)


  • is the set of values.

Description

  • This function gives the value of LU Decomposition of a given matrix.
  • In , is any square matrix.
  • LU Decomposition is the procedure for decomposing any square matrix in to a product of Lower Triangular matrix and Upper Triangular matrix.
  • In LU Decomposition, L stands for Lower Triangular matrix and U stands for Upper Triangular matrix.
  • So A=LU.But sometimes the product includes Permutation Matrix also(PA=LU).
  • LU Decomposition is also called LU Factorization.Here given matrix is split in to lower triangular and Upper triangular matrix.
    • For 2x2 matrix,

  • For 3x3 matrix,

Examples

Spreadsheet
A B
1 4 3
2 6 3

=LUDECOMPOSITION(A1:B2)

1 0
0.6666666666666666 1
6 3
0 1
0 1
1 0
Spreadsheet
A B C
1 1 2 3
2 4 5 6
3 7 8 9

=LUDECOMPOSITION(A1:C3)

1 0 0
0.5714285714285714 1 0
0.14285714285714285 1.999999999999999 1
7 8 9
0 0.4285714285714288 0.8571428571428577
0 0 0
0 0 1
0 1 0
1 0 0

Related Videos

LU Decomposition

See Also

References