Riccati

Given two matrices <code>M</code> and <code>S</code>, solve Riccati equation by iterative updating to find the solution $\mathbf{R}$, where the latter satisfies
$$\mathbf{R}=\mathbf{M}\mathbf{R}\mathbf{M}^\top + \mathbf{S}$$
until convergence (i.e., when the Frobenius norm is less than <code>tol</code>, or the maximum number of iterations <code>maxiter</code> is reached.

Kernel smoothing for Wishart random matrices described in Daayeb, Khardani and Ouimet (2025) <doi:10.48550/arXiv.2506.08816>, Gaussian and log-Gaussian models using least square or likelihood cross validation criteria for optimal bandwidth selection.

Leo Belzile

Kernel Density Estimation for Random Symmetric Positive Definite
Matrices

Frederic Ouimet

Riccati function

<dl><dt>M</dt>
<dd>matrix</dd>
<dt>S</dt>
<dd>matrix</dd>
<dt>tol</dt>
<dd>double for tolerance</dd>
<dt>maxiter</dt>
<dd>integer, the maximum number of iterations</dd></dl>

Arguments

Solver for Riccati equation — Riccati

<dl>

<dt>M</dt>
<dd>matrix</dd>


<dt>S</dt>
<dd>matrix</dd>


<dt>tol</dt>
<dd>double for tolerance</dd>


<dt>maxiter</dt>
<dd>integer, the maximum number of iterations</dd>

</dl>

Riccati: Solver for Riccati equation

Description

Usage

Value

Arguments