01-15-2019, 10:42 PM
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Hi, all:
Welcome to my brand new SRC#003, this time commemorating the New Year 2019.
There will be some (hopefully) interesting things discussed here but first of all there's a simple assignment for you to tackle with your preferred HP calculator (not Excel, Matlab, Mathematica, Python, Java, Haskell, Wolfram Alpha, etc., there are other forums/threads for that), namely:
Write a program which implements the following procedure:
1) Create this 3x3 matrix M:
| \(\pi\) 2019 2019 |
M = | 1 \(\pi\) 2019 |
| 1 1 \(\pi\) |
2) Compute the successive powers of M (i.e: M2, M3, etc.) and for each power n compute the value of Mn(1,3) / Mn(2,3) until it converges to some limit.
What is the numerical value of this limit ? What do you think this procedure is actually computing ?
You can use any HP calculator of your choice (Minimum Recommended Model would be the HP-11C or better) but, again, write your code only in RPN, RPL or 71-BASIC, please, and it would be better if you don't peruse the Internet, just your programming skills and math intuition.
In a few days I'll give a 5-line, 144-byte program for the HP-71B (easiest code to understand), plus extensive comments and further discussion.
Meanwhile, let's see what you come up with.
V.
.
Hi, all:
Welcome to my brand new SRC#003, this time commemorating the New Year 2019.
There will be some (hopefully) interesting things discussed here but first of all there's a simple assignment for you to tackle with your preferred HP calculator (not Excel, Matlab, Mathematica, Python, Java, Haskell, Wolfram Alpha, etc., there are other forums/threads for that), namely:
Write a program which implements the following procedure:
1) Create this 3x3 matrix M:
| \(\pi\) 2019 2019 |
M = | 1 \(\pi\) 2019 |
| 1 1 \(\pi\) |
2) Compute the successive powers of M (i.e: M2, M3, etc.) and for each power n compute the value of Mn(1,3) / Mn(2,3) until it converges to some limit.
What is the numerical value of this limit ? What do you think this procedure is actually computing ?
You can use any HP calculator of your choice (Minimum Recommended Model would be the HP-11C or better) but, again, write your code only in RPN, RPL or 71-BASIC, please, and it would be better if you don't peruse the Internet, just your programming skills and math intuition.
In a few days I'll give a 5-line, 144-byte program for the HP-71B (easiest code to understand), plus extensive comments and further discussion.
Meanwhile, let's see what you come up with.
V.
.