Reference · The Applied Higher-Order Functions catalogue

rainbow.algorithms.proofs.ahof.secant

The Applied Higher-Order Functions cataloguesrc/rainbow/algorithms/proofs/ahof/secant.clj3 definitions, 3 theorems

AHoF O27 Secant Method: root-find by the secant update x - f(x)*(x-x_prev)/(f-f_prev); the divided-difference denominator is the value change value-change f-new f-old = f-new - f-old. Worked: 4-1=3. Values proved by signed cross-product equivalence. Proved native and axiom-free. Requires signed/subtract, signed/from-nnrat, signed/equivalent (all in the D63 checkpoint). Scope (measured by the kernel): this module has 2 worked instances (statements about specific values) and 1 definitional unfoldings (true by unfolding a definition). None of its theorems is a guarantee about the algorithm for all inputs; `lein verify rainbow.algorithms.proofs.ahof.secant` prints this classification.

secant/value-change :
  (x₁ x₂ : ℚ)
  → ℚ

secant/change-example :
  → ℚ

secant/no-change :
  → ℚ

secant/value-change-unfold :
  (a b : ℚ)
  → nat-grad/update a b = a - b

secant/change-example-is-3 :
  → bfgs/change-example = signed/from-nnrat 3

secant/no-change-is-0 :
  → dfp/no-step = signed/from-nnrat 0