How to make sure singularity is avoided when numerically solving inverse kinematics?

Hello Robotics community,

I am trying to understand Jacobian-based numerical inverse kinematic methods. I read about Jacobian pseudo inverse and Jacobian transpose methods. I am not sure how singularities are avoided or large changes in the joints between solution steps. Can you recommend a resource that discusses/implements those methods in more detail or share from your experience?

Thank you!