The answers previously given are correct for AI which can indeed process more information with more computational power. However, actual reasoning ability like humans have is not defined by Church-Turing. AIXI has nothing to do with human reasoning. A pretty good clue to this fact is that AIXI has been around since 2005 and to date there are no machines based on it that have human-level reasoning. For example, an interesting topic in AI is natural language processing (NLP). I can speak into my Android phone and it will transcribe my speech into text. It seems like an amazing advance. However, this is what a human would do if they heard a foreign language and then did a phonetic transcription of what they heard. Then they looked up a phonetic chart to match the sounds with words. This would take place without any actual understanding of what they were hearing. This is how it works on my phone, much like Searle's Chinese Room.
Humans are quite different because they actually understand words. The equivalent to this in AI would be natural language understanding (NLU). No AI today has NLU and no theory within AI explains how to construct it. There isn't any research on AI NLU because there is no starting point. A fact that most AI enthusiasts don't like to admit is that even the smartest AI systems are routinely outclassed by rats and even six month old babies in terms of comprehension. AI systems have no comprehension or understanding and without this they have no actual reasoning ability. Human-level comprehension falls under a completely different theory from the computational derivatives of Church-Turing.
Can you make a human-level machine agent smarter by giving it more computational power? No, because you'll run into all sorts of problems which would take a few book chapters to explain. There are enhancements you can make but these have limits. If you go by a standard deviation 15 chart for IQ like Wechsler or the 5th edition of Stanford-Binet, the chances of having an IQ of 195 is 1 out of 8 billion. So, this roughly sets the upper bound of human ability. We could probably see machine agents with an IQ of 240 but not 500 or 1,000. I do understand the confusion concerning computation since exhaustive routines in AI are time limited. For example, our dim-witted chess programs play by laborious trial and error. They don't actually get smarter with more computational power, they are just able to eliminate bad moves faster. Let me give a human example. Let's say that I could do 5 math problems of a given complexity per hour using pencil and paper. So, I add a slide rule and my rate changes to 10 problems per hour. Then I switch to a calculator and my rate increases to 20. Let's say I then start using a spreadsheet and I hit 30 per hour. I am not actually 6x smarter than I was when I used pencil and paper.
So, to answer the question, it is not possible to continuously increase intelligence even with unlimited computational power. However, it should be possible for machine intelligence to exceed human intelligence. One final thing that I should mention though is that this type of theory is quite good at organizing knowledge in a way that current big data methods do not. So, it is probable that the same theory that would allow a machine IQ of 240 would also provide enough assistance to a human to function at the same level.