LU decomposition with pivoting and inverse with LU

LU decomposition with pivoting and inverse with LUYas Ahmad Adha (14/370755/PTK/9687)Dwi Novianto (13/356779/PTK/09210)Majid Rahardi (14/376446/PTK/10149)Group 6LU decomposition with pivoting To find the value of [L] and [U]Permutation Matrix: a permutation matrix P is I with rows permuted (simple mode)Unique [P]-1 = [P]T[P][A] = [L][U][P] = track of row swapsFind the value of largest pivot elementAbs pivot elementElimination and substritusi opposite of multiplayernya

Example LU with Pivot

http://math.stackexchange.com/questions/485513/what-are-pivot-numbers-in-lu-decomposition-please-explain-me-in-an-examplefind the value of [L] and [U] with pivoting?

Example LU with Pivot

http://math.stackexchange.com/questions/485513/what-are-pivot-numbers-in-lu-decomposition-please-explain-me-in-an-exampleExample LU with Pivot

http://math.stackexchange.com/questions/485513/what-are-pivot-numbers-in-lu-decomposition-please-explain-me-in-an-exampleExample LU with Pivot

http://math.stackexchange.com/questions/485513/what-are-pivot-numbers-in-lu-decomposition-please-explain-me-in-an-exampleinverse with LULU Decomposition Method to find inverse of A square matrixDeterminan 0[A]nxn . [A]-1nxn = [I]nxn Decomposition [A] = [L] [U] [X] = [A] -1[L] [Z] = [C][U] [X] = [Z]

inverse with LUa11a12a13a14a21a22a23a24a31a32a33a34a41a42a43a44x11x12x13x14x21x22x23x24x31x32x33x34x41x42x43x441000010000100001AAI1000l21100l31l3210l41l42l431u11u12u13u140u22u23u2400u33u34000u44LUx11x21x31x41X1000CStep 1 [L] [Z] = [C]

[U] [X] = [Z]1000l21100l31l3210l41l42l431Z1Z2Z3Z41000u11u12u13u140u22u23u2400u33u34000u44x11x21x31x41Z1Z2Z3Z4Forward SubtitutionBack SubtitutionStep 2 [L] [Z] = [C]

[U] [X] = [Z]1000l21100l31l3210l41l42l431Z1Z2Z3Z40100u11u12u13u140u22u23u2400u33u34000u44x12x22x32x42Z1Z2Z3Z4Cotinue this process forAll the n column of the [B] matrixExample Inverse

find the inverse value matrix [A] ?

Already know [L] and [U]

Example

Example

Example