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Scilabヘルプ >> Linear Algebra > Matrix Pencil > penlaur

# penlaur

### 呼び出し手順

```[Si,Pi,Di,order]=penlaur(Fs)
[Si,Pi,Di,order]=penlaur(E,A)```

Fs

E, A

Si,Pi,Di

order

### 説明

`penlaur` は,無限大における `(s*E-A)^-1`の最初のローラン係数を 計算します.

`(s*E-A)^-1 = ... + Si/s - Pi - s*Di + ...` at .

`s` = 無限大における `order` = 特異点の次数 (order=index-1).

より大きな添字のペンシルの場合, 項 `-s^2 Di(2), -s^3 Di(3),...` は次のように指定されます:

`Di(2)=Di*A*Di`, `Di(3)=Di*A*Di*A*Di` (最大 `Di(order)`).

### 例

```F=randpencil([],[1,2],[1,2,3],[]);
F=rand(6,6)*F*rand(6,6);[E,A]=pen2ea(F);
[Si,Pi,Di]=penlaur(F);
[Bfs,Bis,chis]=glever(F);
norm(coeff(Bis,1)-Di,1)```

### 参照

• glever — 行列ペンシルの逆
• pencan — 行列ペンシルの正準形
• rowshuff — シャッフルアルゴリズム

### Comments

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