This invention discloses a floating-point-fractional
hybrid anchoring method and computational
system for suppressing iteration errors, belonging to the field of high-precision numerical computation technology. It solves the technical problems of pseudo-chaos caused by the accumulation of iteration errors in pure floating-point calculations, the computational power explosion in pure high-precision fractional calculations, and the inability to simultaneously achieve both computational power and precision. This invention completes high-speed iterative computations of nonlinear systems using a general floating-point format. After each floating-point calculation, an optimal rational number
approximation algorithm is used to convert the calculation result into a simplified rational number with a denominator not exceeding a preset threshold, eliminating the original errors introduced by floating-point truncation and
rounding. The purified rational number is then converted back to floating-point format to participate in the next iteration, relying on a bounded rational number anchoring mechanism to progressively block the error amplification chain. The denominator threshold is set to 10¹²~10¹ based on the
effective number of bits of the floating-point number. 5 This invention can adaptively adjust to various scenarios such as embedded terminals, supercomputing, and industrial control, and optimizes the continued fraction
algorithm to achieve the globally optimal rational approximation under a given upper limit of the denominator. It requires no dedicated large number hardware and combines the advantages of high-speed, low-load floating-point operations with zero
approximation error in rational numbers. It can be stably used in nonlinear computing scenarios that are sensitive to initial values and require long-term stable iterations, such as
chaotic simulation, vehicle trajectory prediction, industrial PID closed-
loop control, 5G / 6G
communication channel simulation, microscale meteorological
simulation, and large-scale number theory zero-point
verification. It effectively eliminates numerical trajectory drift, reduces equipment computing
power consumption, and minimizes the
workload of manual calibration and data screening, possessing extremely high
engineering and academic application value.