Fish growth and water quality go hand in hand but not from a nutrition standpoint. Micro and macro nutrients in the water are more for a planted tank and marine tanks with coral. The plants are what would benefit from the nutrients in the water and the coral as well from the minerals etc. Large frequent water changes keeps accumulated nitrate and other chemicals at bay, thus providing a healthy environment for aquatic inhabitants. That being said, nutrition does play an important role in proper growth. I said proper because one could feed goldfish high fatty content and the fish will show accelerated growth, even abnormal but at the cost of the fishs' well being and longevity. Some fish grow fast just because they are genetically predisposed to do so and accelerating that could be harmful. Some fish will grow slow no matter what you do.
Its good to keep in mind that we are caretakers and not divine entities. We want our fish to be spectacular specimens but not at the expense of health, fish cost to much to have them meet an early demise. When doing water changes, keep in mind you are removing toxins in the water. Remove all the water, remove all toxins right? How do you remove as much toxins as possible without removing all the water? Frequently remove portions of the water. Try 10% once a week. Note the nitrate level. Then after a few water changes, remove 15% once a week. Note the difference in nitrate reduction and monitor through a few more water changes. Keep this regimen until you arent producing nitrate over a safe level. A good place to start is reading about and understanding the nitrogen cycle found online...Google my friend.
Good Luck.