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2024.1.0 - 日本語


sylv

シルベスタ式 A*X + X*B = C または A*X*B + X = C を解決します

呼び出し手順

sylv(A, B, C, 'c')
sylv(A, B, C, 'd')

引数

A, B, C

適当な次元の実数行列.

flag 'c' or 'd'

文字列 ('c' または 'd')

説明

X = sylv(A, B, C, 'c') は以下の "連続時間" シルベスタ方程式の解Xを計算します, A*X + X*B = C.

X = sylv(A, B, C, 'd') は以下の "離散時間" シルベスタ方程式の解Xを計算します, A*X*B + X = C.

X = -sylv(-A, B, C, 'd') computes X as solution of the real "discrete time" Sylvester equation A*X*B - X = C.

A = rand(4, 4); C = rand(4, 3); B = rand(3, 3);

// Continuous time Sylvester equation:
X = sylv(A, B, C, 'c');
norm(A*X + X*B - C)

// Modified Discrete time Sylvester equation:
X = sylv(A, B, C, 'd');
norm(A*X*B - X - C)

 // Real Discrete time Sylvester equation:
X = -sylv(-A, B, C, 'd');
norm(A*X*B - X - C)

参考

  • lyap — リアプノフ方程式
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Last updated:
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