New default values

Author: DaniGlez

lib/SimpleNonlinearSolve/src/bracketing/itp.jl

@@ -17,13 +17,13 @@ The following keyword parameters are accepted.
   - `n₀::Int = 10`, the 'slack'. Must not be negative. When n₀ = 0 the worst-case is
     identical to that of bisection, but increacing n₀ provides greater oppotunity for
     superlinearity.
-  - `κ₁::Float64 = 0.007`. Must not be negative. The recomended value is `0.2/(x₂ - x₁)`.
+  - `scaled_κ₁::Float64 = 0.2`. Must not be negative. The recomended value is `0.2`.
     Lower values produce tighter asymptotic behaviour, while higher values improve the
     steady-state behaviour when truncation is not helpful.
-  - `κ₂::Real = 1.5`. Must lie in [1, 1+ϕ ≈ 2.62). Higher values allow for a greater
+  - `κ₂::Real = 2`. Must lie in [1, 1+ϕ ≈ 2.62). Higher values allow for a greater
     convergence rate, but also make the method more succeptable to worst-case performance.
-    In practice, κ=1,2 seems to work well due to the computational simplicity, as κ₂ is used
-    as an exponent in the method.
+    In practice, κ=1, 2 seems to work well due to the computational simplicity, as κ₂ is
+    used as an exponent in the method.
 
 ### Worst Case Performance
 
@@ -35,19 +35,19 @@ n½ + `n₀` iterations, where n½ is the number of iterations using bisection
 If `f` is twice differentiable and the root is simple, then with `n₀` > 0 the convergence
 rate is √`κ₂`.
 """
-struct ITP{T} <: AbstractBracketingAlgorithm
-    k1::T
-    k2::T
+struct ITP{T₁, T₂} <: AbstractBracketingAlgorithm
+    scaled_k1::T₁
+    k2::T₂
     n0::Int
-    function ITP(; k1::Real = 0.007, k2::Real = 1.5, n0::Int = 10)
-        k1 < 0 && error("Hyper-parameter κ₁ should not be negative")
+    function ITP(;
+            scaled_k1::T₁ = 0.2, k2::T₂ = 2, n0::Int = 10) where {T₁ <: Real, T₂ <: Real}
+        scaled_k1 < 0 && error("Hyper-parameter κ₁ should not be negative")
         n0 < 0 && error("Hyper-parameter n₀ should not be negative")
         if k2 < 1 || k2 > (1.5 + sqrt(5) / 2)
             throw(ArgumentError("Hyper-parameter κ₂ should be between 1 and 1 + ϕ where \
                                  ϕ ≈ 1.618... is the golden ratio"))
         end
-        T = promote_type(eltype(k1), eltype(k2))
-        return new{T}(k1, k2, n0)
+        return new{T₁, T₂}(scaled_k1, k2, n0)
     end
 end
 
@@ -72,7 +72,7 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::ITP, args...;
     end
     ϵ = abstol
     #defining variables/cache
-    k1 = alg.k1
+    k1 = alg.scaled_k1 / abs(right - left)
     k2 = alg.k2
     n0 = alg.n0
     n_h = ceil(log2(abs(right - left) / (2 * ϵ)))
@@ -88,7 +88,7 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::ITP, args...;
     while i <= maxiters
         span = abs(right - left)
         r = ϵ_s - (span / 2)
-        δ = k1 * (span^k2)
+        δ = k1 * ((k2 == 2) ? span^2 : (span^k2))
 
         ## Interpolation step ##
         x_f = left + (right - left) * (fl / (fl - fr))