An iterative procedure for solving the Riccati equation \(A_2R-RA_1 = A_3+RA_4R\) (Q2717716)
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scientific article; zbMATH DE number 1605306
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | An iterative procedure for solving the Riccati equation \(A_2R-RA_1 = A_3+RA_4R\) |
scientific article; zbMATH DE number 1605306 |
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17 June 2001
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iterative procedure
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operator Riccati equation
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quadratic convergence
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spectral approximation
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Banach spaces
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An iterative procedure for solving the Riccati equation \(A_2R-RA_1 = A_3+RA_4R\) (English)
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The author presents an iterative procedure to obtain approximations for the solution \(R\in \text{BL}(X_1, X_2)\) of the Riccati equation NEWLINE\[NEWLINEA_2 R- RA_1= A_3+ RA_4 R,NEWLINE\]NEWLINE where \(X_1\), \(X_2\) are complex Banach spaces, \(A_1\in \text{BL}(X_1)\), \(A_2\in \text{BL}(X_2)\), \(A_3\in \text{BL}(X_1, X_2)\) and \(A_4\in \text{BL}(X_2, X_1)\). It is shown that the convergence of the method is quadratic. An application of the procedure to spectral approximation under perturbation of the operator is made.
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0.7839333415031433
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0.7839333415031433
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