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

in COMPUTINGTHEEQUILIBRIAOFDYNAMIC COMMONPROPERTYGAMES putingtheequilibriaofaclassofdynamiclinear-quadraticgamesAbstract.Inthispaper,wediscusstechniquesforrapidlycom- ETHANLIGONANDURVASHINARAIN
by Anal- Thisclassofgameshasbeenmuchstudied, Thesearchforequilibria Ysisofthegamehastendedtofocusonitssteady-stateproperties Involvingtheextracti, Inthispaperwedescribeatechniqueforcomputingmarkovperfect Introduction
"... 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

in On the Mechanics of Forming and Estimating Dynamic Linear Economies
by Evan W. Anderson, Lars Peter Hansen, Ellen R. McGrattan, Thomas J. Sargent 1996
Cited by 11

TABLE I GENERAL KALMAN FILTER RECURSIONS BASED ON THE RICCATI EQUATIONS

in unknown title
by unknown authors 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 The Sampled-Data H∞ Problem: A Unified Framework for Discretization Based Methods and Riccati Equation Solution
by H. T. Toivonen, M. F. Sagfors
"... 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.

in Numerical methods in control, from pole assignment via linear quadratic to H infinity control
by Volker Mehrmann, Hongguo Xu

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

in A Multi-Level Technique For The Approximate Solution Of Opertaor Lyapunov And Riccati Equations
by C. Wang, Southern California, I. G. Rosen, I. G. Rosen, Chunming Wang 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.

in A Multi-Grid Method for Generalized Lyapunov Equations
by Thilo Penzl 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

in {UniversiteCatholiquedeLouvain,Belgium.
by B^at. Bsystemes Grandetraverse Liege Belgium

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

in Solution of Algebraic Riccati Equations Arising in Control of Partial Differential Equations
by Kirsten Morris, Carmeliza Navasca
"... 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 A Genetic Algorithm Compared With a Gradient-Based Method for the Solution of an Active-Control Model Problem
by Nathalie Marco, Cyril Godart, Jean-Antoine Desideri, Bertrand Mantel, Jacques Periaux
"... 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;.... ..."
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