#24313·scipy

BUG: sparse.linalg.minres: residual increases when given more iterations for low rtol values

Author: ReallyCoolNameCreated Jan 9, 2026Updated Sep 18, 2026

Labelsdefectscipy.sparse.linalg

Describe your issue.

The residual for res1 = sparse.linalg.minres(Amat,bvec,rtol=1e-14,check=True,maxiter=1000)

is larger than the residual from res2 = sparse.linalg.minres(Amat,bvec,rtol=1e-14,check=True,maxiter=4000)

(by over 4 orders of magnitude)

However for rtol=1e-10 there is no problem.

The data (and the python script to test it) are available here (I'd have posted a small example, but I couldn't reproduce the problem for a reasonably small matrix I could post here)

Reproducing Code Example

python

import numpy as np
from scipy import sparse

Amat = np.load("Amat.npy")
bvec = np.load("bvec.npy")

Amat = sparse.csr_array(Amat)

res1 = sparse.linalg.minres(Amat,bvec,rtol=1e-14,check=True,maxiter=1000)

res2 = sparse.linalg.minres(Amat,bvec,rtol=1e-14,check=True,maxiter=4000)

print(f"Exit reason for 1000 iteration test: {res1[1]}\nExit reason for 4000 iteration test: {res2[1]}")
print(f"Residual for 1000 iteration test: {np.linalg.norm((Amat @ res1[0][:,np.newaxis])-bvec)}\nResidual for 4000 iteration test: {np.linalg.norm((Amat @ res2[0][:,np.newaxis])-bvec)}")

Error message

bash

No errors.

SciPy/NumPy/Python version and system information

bash

1.16.3 1.26.4 sys.version_info(major=3, minor=12, micro=4, releaselevel='final', serial=0)
Build Dependencies:
  blas:
    detection method: pkgconfig
    found: true
    include directory: C:/Users/runneradmin/AppData/Local/Temp/cibw-run-0_as6mvx/cp312-win_amd64/build/venv/Lib/site-packages/scipy_openblas32/include
    lib directory: C:/Users/runneradmin/AppData/Local/Temp/cibw-run-0_as6mvx/cp312-win_amd64/build/venv/Lib/site-packages/scipy_openblas32/lib
    name: scipy-openblas
    openblas configuration: OpenBLAS 0.3.29.dev DYNAMIC_ARCH NO_AFFINITY Haswell MAX_THREADS=24
    pc file directory: D:/a/scipy/scipy
    version: 0.3.29.dev
  lapack:
    detection method: pkgconfig
    found: true
    include directory: C:/Users/runneradmin/AppData/Local/Temp/cibw-run-0_as6mvx/cp312-win_amd64/build/venv/Lib/site-packages/scipy_openblas32/include
    lib directory: C:/Users/runneradmin/AppData/Local/Temp/cibw-run-0_as6mvx/cp312-win_amd64/build/venv/Lib/site-packages/scipy_openblas32/lib
    name: scipy-openblas
    openblas configuration: OpenBLAS 0.3.29.dev DYNAMIC_ARCH NO_AFFINITY Haswell MAX_THREADS=24
    pc file directory: D:/a/scipy/scipy
    version: 0.3.29.dev
  pybind11:
    detection method: config-tool
    include directory: unknown
    name: pybind11
    version: 3.0.1
Compilers:
  c:
    commands: cc
    linker: ld.bfd
    name: gcc
    version: 10.3.0
  c++:
    commands: c++
    linker: ld.bfd
    name: gcc
    version: 10.3.0
  cython:
    commands: cython
    linker: cython
    name: cython
    version: 3.1.6
  fortran:
    commands: gfortran
    linker: ld.bfd
    name: gcc
    version: 10.3.0
  pythran:
    include directory: C:\Users\runneradmin\AppData\Local\Temp\build-env-dfcay8wl\Lib\site-packages/pythran
    version: 0.18.0
Machine Information:
  build:
    cpu: x86_64
    endian: little
    family: x86_64
    system: windows
  cross-compiled: false
  host:
    cpu: x86_64
    endian: little
    family: x86_64
    system: windows
Python Information:
  path: C:\Users\runneradmin\AppData\Local\Temp\build-env-dfcay8wl\Scripts\python.exe
  version: '3.12'

Source: scipy/scipy

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