### Table 1. Code to solve matrix algebraic pseudo-Riccati equation

"... In PAGE 11: ... Code to solve matrix pseudo-Riccati di er- ence equation The law of motion for the resource is simply xt+1 = xt ? y1t ? y2t; so we choose A = I2, B = (?1; 0)0, C = (?1; 0)0. Supplying this parameters to the maple program listed in Table1... ..."

### Table 9.2: Performance of Algorithms that Solve Riccati Equations

1996

Cited by 11

### TABLE I GENERAL KALMAN FILTER RECURSIONS BASED ON THE RICCATI EQUATIONS

1998

Cited by 8

### Table 1. Parameters of the equivalent discrete system representation (16) and the solutions to the discrete Riccati equations (61) and (82) for three values of .

"... In PAGE 24: ...ot change sign in the interval [0; h), cf. Theorem 5.4 and Remark 5.1. Table1 shows the parameters of the equivalent discrete system representations. It is interesting to note that for the values of shown in the example, the discrete systems are unsta- ble, although the continuous-time system (104) is stable.... ..."

### Table 2 We see that the direct computation of the optimal control via the subspace yields much smaller relative errors than the solution via the Riccati equation. Note that the subspace method always computed the Riccati solution to high relative accuracy.

### Table 5.3: Number of Smith iterations in solving matrix Riccati equation, n = 62 Newton # of Smith Iterations Iteration p1 = 7 p2 = 15 p3 = 30 p4 = 61 n = 62

1995

Cited by 15

### Table 4: Test 3. Numbers of multi-grid iterations depending on lmax in Newton Steps 1{5. Although the dimension of the problem is increasing relatively fast, the number of multi-grid iterations remains nearly constant in each Newton step. It might be possible to solve the Riccati equation with less multi-grid iterates using other stopping criteria for the multi-grid iterations within the Newton iteration. For example, we could solve the Lyapunov equations in the rst Newton steps less accurate than those in the last steps. Unfortunately, this involves the danger of a convergence in the Newton method towards one of the non-stabilizing solutions of the Riccati equation. However, this has not been observed in our numerical experiments.

1997

Cited by 1

### Table 1: Comparison of methods for invariant subspace computation. The last column gives the numeri- cal cost by iteration for A block tridiagonal (see Section 5). \Newton on Gr(p; n) quot; refers to the Newton algo- rithm [Smi94] on the manifold Gr(p; n) for nding a stationary point of a generalized version of the classical Rayleigh quotient A(bY c) = tr (Y T Y )?1Y T AY . In [Dem87], Demmel uni es algorithms from [Cha84, DMW83, Ste73] by showing that they all attempt to solve the same Riccati equation A22K ? KA11 = ?A21 + KA12K; (28) which solves the invariant subspace problem AZ ? ZB = 0

### Table 2. Heat Equation: Feedback Gain at each Newton-Kleinman Iteration

"... In PAGE 6: ... The solutions to the approximating Riccati equations converge [3, 13]and so do the feedback operators. Table2 shows the approximated optimal feedback gain at each Newton-Kleinman iteration. The data in Table 2 is identical for n = 25; 50; 100; 200 and for both Newton-Kleinman methods.... In PAGE 6: ... Table 2 shows the approximated optimal feedback gain at each Newton-Kleinman iteration. The data in Table2 is identical for n = 25; 50; 100; 200 and for both Newton-Kleinman methods. The error in K versus Newton-Kleinman iteration in shown in Figure 1 for standard Newton- Kleinman and in Figure 2 for the modifled algorithm.... ..."

### Table 3 : Riccati solution vs Genetic Algorithm with Riccati initialization, when quot; is not small.

"... In PAGE 27: ...e less) than those obtained with the random initialization. By comparing with the Riccati solution, the cost functionals, for quot; 10?2, are bet- ter with the genetic approach (see Table3 ), but when quot; becomes smaller, the Riccati method gives better results (see Table 4). The di erent controls obtained with the Ge- netic Algorithm with Riccati initialization are presented on Figure 15, for the di erent values of quot;.... ..."