Merge pull request #198 from yash2798/ys/itp_docs

Updating docs and tutorials for ITP

Author: ChrisRackauckas

README.md

@@ -32,7 +32,7 @@ solver = solve(probN, NewtonRaphson(), abstol = 1e-9)
 f(u, p) = u .* u .- 2.0
 u0 = (1.0, 2.0) # brackets
 probB = IntervalNonlinearProblem(f, u0)
-sol = solve(probB, Falsi())
+sol = solve(probB, ITP())
 ```
 
 ## v1.0 Breaking Release Highlights!

docs/src/solvers/BracketingSolvers.md

@@ -7,8 +7,7 @@ Solves for ``f(t)=0`` in the problem defined by `prob` using the algorithm
 
 ## Recommended Methods
 
-`Falsi()` can have a faster convergence and is discretely differentiable, but is
-less stable than `Bisection`.
+`ITP()` is the recommended method for the scalar interval root-finding problems. It is particularly well-suited for cases where the function is smooth and well-behaved; and achieved superlinear convergence while retaining the optimal worst-case performance of the Bisection method. For more details, consult the detailed solver API docs. 
 `Ridder` is a hybrid method that uses the value of function at the midpoint of the interval to perform an exponential interpolation to the root. This gives a fast convergence with a guaranteed convergence of at most twice the number of iterations as the bisection method.
 `Brent` is a combination of the bisection method, the secant method and inverse quadratic interpolation. At every iteration, Brent's method decides which method out of these three is likely to do best, and proceeds by doing a step according to that method. This gives a robust and fast method, which therefore enjoys considerable popularity.
 
@@ -19,6 +18,7 @@ less stable than `Bisection`.
 These methods are automatically included as part of NonlinearSolve.jl. Though, one can use
 SimpleNonlinearSolve.jl directly to decrease the dependencies and improve load time.
 
+  - `ITP`: A non-allocating ITP (Interpolate, Truncate & Project) method
   - `Falsi`: A non-allocating regula falsi method
   - `Bisection`: A common bisection method
   - `Ridder`: A non-allocating Ridder method

src/trustRegion.jl

@@ -11,6 +11,7 @@ end
 TrustRegion(; chunk_size = Val{0}(), autodiff = Val{true}(),
             standardtag = Val{true}(), concrete_jac = nothing,
             diff_type = Val{:forward}, linsolve = nothing, precs = DEFAULT_PRECS,
+            radius_update_scheme = RadiusUpdateSchemes.Simple,
             max_trust_radius::Real = 0 // 1,
             initial_trust_radius::Real = 0 // 1,
             step_threshold::Real = 1 // 10,