X Meme MINE 1) Exercise 4.4 in the textbook. You may want to use portti time.pert contents toc timer unter tie in seconds to the 2) Give the standard (IEEE) single precision binary representation of the machine approximation for -13. Don't find an algorithm to do this, but write it out yourself 3) Find the smallest positive integer that is not exact in single precision Show your work 4) What are the two's complement representations for these decimal numbers? Use 12 bits 9 455, 1021.-12.-1022-1023 5) What are the octal binary and hexadecimal representations of the decimal numbers 132 133 1333 and 133337 Show your work erations, which could take hours to complete. Thus the largest matrices we Piano in practice take the limit No, but we can make a reasonable approxima- Interestingly, the direct mai multiplication represented by the code aytest way to multiply two matrices on a computer Sms multiplying matrices that some clever shortcuts to reduce there that the total number is proportional about Nrather than N. For veya result in significantly faster computation. Unfortunately, then numerical ene bene of pooblems with subtraction of early alhes and for this on it is alysed, Opper, an thad for the Canadian which is a ter of peace hot but in practice this method is complex to proces extra complexity that in applications the method is always had and X=-1+hk multiply are about 1000 x 1000 in size. where sie by just making N large. Exercise 4.4: Calculating integrals Suppose we want to calculate the value of the integral 1 - v1 zdr. The integrand looks like a semicircle of radius 1: Write a program to evaluate the integral above with N = 100 and compare the result with the exact value. The two will not agree very well, because N = 100 is not a sufficiently large number of slices. Increase the value of N to get a more accurate value for the integral. If we require that the program runs in about one second or less, how accurate a value can you get? Frating integrals is a common task in computational physics calculations. We will tady techniques for doing integrals in detail in the next chapter. As we will see, there substantially quicker and more accurate methods than the simple one we have used -1 D 1.57079632679... and hence the value of the integral--the area under the curve-must begin Alternatively, we can evaluate the integral on the computer by dividing the derde of integration into a large number of slices of width = 2/Noach and the only the Riemann definition of the integral: lim cation X Meme MINE 1) Exercise 4.4 in the textbook. You may want to use portti time.pert contents toc timer unter tie in seconds to the 2) Give the standard (IEEE) single precision binary representation of the machine approximation for -13. Don't find an algorithm to do this, but write it out yourself 3) Find the smallest positive integer that is not exact in single precision Show your work 4) What are the two's complement representations for these decimal numbers? Use 12 bits 9 455, 1021.-12.-1022-1023 5) What are the octal binary and hexadecimal representations of the decimal numbers 132 133 1333 and 133337 Show your work erations, which could take hours to complete. Thus the largest matrices we Piano in practice take the limit No, but we can make a reasonable approxima- Interestingly, the direct mai multiplication represented by the code aytest way to multiply two matrices on a computer Sms multiplying matrices that some clever shortcuts to reduce there that the total number is proportional about Nrather than N. For veya result in significantly faster computation. Unfortunately, then numerical ene bene of pooblems with subtraction of early alhes and for this on it is alysed, Opper, an thad for the Canadian which is a ter of peace hot but in practice this method is complex to proces extra complexity that in applications the method is always had and X=-1+hk multiply are about 1000 x 1000 in size. where sie by just making N large. Exercise 4.4: Calculating integrals Suppose we want to calculate the value of the integral 1 - v1 zdr. The integrand looks like a semicircle of radius 1: Write a program to evaluate the integral above with N = 100 and compare the result with the exact value. The two will not agree very well, because N = 100 is not a sufficiently large number of slices. Increase the value of N to get a more accurate value for the integral. If we require that the program runs in about one second or less, how accurate a value can you get? Frating integrals is a common task in computational physics calculations. We will tady techniques for doing integrals in detail in the next chapter. As we will see, there substantially quicker and more accurate methods than the simple one we have used -1 D 1.57079632679... and hence the value of the integral--the area under the curve-must begin Alternatively, we can evaluate the integral on the computer by dividing the derde of integration into a large number of slices of width = 2/Noach and the only the Riemann definition of the integral: lim cation